142:
7451:
3080:
122:
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354:). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. When using the semi-parametric methods, the underlying process is modeled using a non-parametric framework, with the additional assumption that the number of non-zero components of the model is small (i.e., the model is sparse). Similar approaches may also be used for missing data recovery as well as
98:
7475:
130:
7463:
3075:{\displaystyle {\begin{aligned}x_{n}&=\sum _{k}A_{k}\sin(2\pi \nu _{k}n+\phi _{k})\\&=\sum _{k}A_{k}\left(\sin(\phi _{k})\cos(2\pi \nu _{k}n)+\cos(\phi _{k})\sin(2\pi \nu _{k}n)\right)\\&=\sum _{k}\left(\overbrace {a_{k}} ^{A_{k}\sin(\phi _{k})}\cos(2\pi \nu _{k}n)+\overbrace {b_{k}} ^{A_{k}\cos(\phi _{k})}\sin(2\pi \nu _{k}n)\right)\end{aligned}}}
305:. But the periodogram does not provide processing-gain when applied to noiselike signals or even sinusoids at low signal-to-noise ratios. In other words, the variance of its spectral estimate at a given frequency does not decrease as the number of samples used in the computation increases. This can be mitigated by averaging over time (
1353:
2534:
2388:
267:
representation. Linear operations that could be performed in the time domain have counterparts that can often be performed more easily in the frequency domain. Frequency analysis also simplifies the understanding and interpretation of the effects of various time-domain operations, both linear and
156:
analysis or spectral density estimation, is the technical process of decomposing a complex signal into simpler parts. As described above, many physical processes are best described as a sum of many individual frequency components. Any process that quantifies the various amounts (e.g. amplitudes,
83:
Some SDE techniques assume that a signal is composed of a limited (usually small) number of generating frequencies plus noise and seek to find the location and intensity of the generated frequencies. Others make no assumption on the number of components and seek to estimate the whole generating
4595:
The power spectrum of this example is not continuous, and therefore does not have a derivative, and therefore this signal does not have a power spectral density function. In general, the power spectrum will usually be the sum of two parts: a line spectrum such as in this example, which is not
2229:
2086:
1963:
into a signal subspace and a noise subspace. After these subspaces are identified, a frequency estimation function is used to find the component frequencies from the noise subspace. The most popular methods of noise subspace based frequency estimation are
1134:
2397:
2239:
1015:
313:). Welch's method is widely used for spectral density estimation (SDE). However, periodogram-based techniques introduce small biases that are unacceptable in some applications. So other alternatives are presented in the next section.
4302:
4527:
3312:
3514:
3995:
2097:
526:
3414:
1983:
1890:
3190:
If these data were samples taken from an electrical signal, this would be its average power (power is energy per unit time, so it is analogous to variance if energy is analogous to the amplitude squared).
1558:
are found by treating the YuleâWalker equations as a form of ordinary least squares problem. The Burg estimators are generally considered superior to the YuleâWalker estimators. Burg associated these with
219:
of a function produces a frequency spectrum which contains all of the information about the original signal, but in a different form. This means that the original function can be completely reconstructed
1477:
3185:
3640:
2634:
1064:
3871:
3790:
3687:
1348:{\displaystyle S(f;\phi _{1},\ldots ,\phi _{p},\sigma _{p}^{2})={\frac {\sigma _{p}^{2}\Delta t}{\left|1-\sum _{k=1}^{p}\phi _{k}e^{-2i\pi fk\Delta t}\right|^{2}}}\qquad |f|<f_{N},}
669:
2529:{\displaystyle {\hat {P}}_{\text{MN}}\left(e^{j\omega }\right)={\frac {1}{\left|\mathbf {e} ^{H}\mathbf {a} \right|^{2}}};\ \mathbf {a} =\lambda \mathbf {P} _{n}\mathbf {u} _{1}}
755:
1126:
442:
is a periodogram-based method that uses multiple tapers, or windows, to form independent estimates of the spectral density to reduce variance of the spectral density estimate
1599:
1549:
1508:
876:
792:
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3221:
1091:
321:
Many other techniques for spectral estimation have been developed to mitigate the disadvantages of the basic periodogram. These techniques can generally be divided into
4136:
287:
of the signal, and which provides a mathematical approximation to the full integral solution. The DFT is almost invariably implemented by an efficient algorithm called
2383:{\displaystyle {\hat {P}}_{\text{EV}}\left(e^{j\omega }\right)={\frac {1}{\sum _{i=p+1}^{M}{\frac {1}{\lambda _{i}}}\left|\mathbf {e} ^{H}\mathbf {v} _{i}\right|^{2}}}}
845:
3743:
1379:
342:
or the spectrum of the process without assuming that the process has any particular structure. Some of the most common estimators in use for basic applications (e.g.
3903:
206:
4328:
884:
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3822:
3537:
3110:
2569:
1406:
580:
4101:
3716:
1923:
1787:
1734:
6572:
4672:
Welch, P. D. (1967), "The use of Fast
Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms",
2621:
2595:
4187:
3317:
Again, for simplicity, we will pass to continuous time, and assume that the signal extends infinitely in time in both directions. Then these two formulas become
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4179:
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given assumptions about the number of the components. This contrasts with the general methods above, which do not make prior assumptions about the components.
141:
7227:
6851:
5492:
4431:
208:) are particularly well-suited for this sub-division. General mathematical techniques for analyzing non-periodic functions fall into the category of
6625:
2623:
is a time series (discrete time) with zero mean. Suppose that it is a sum of a finite number of periodic components (all frequencies are positive):
7064:
3229:
3425:
3911:
7501:
2224:{\displaystyle {\hat {P}}_{\text{MU}}\left(e^{j\omega }\right)={\frac {1}{\sum _{i=p+1}^{M}\left|\mathbf {e} ^{H}\mathbf {v} _{i}\right|^{2}}}}
398:
3223:
If the average power is bounded, which is almost always the case in reality, then the following limit exists and is the variance of the data.
1699:
the (possibly complex) frequency components of a received signal (including transmitted signal and noise), one uses a multiple-tone approach.
7516:
5107:
5086:
5067:
4938:
4826:
4789:
5487:
5187:
4605:
1685:
6091:
5239:
2081:{\displaystyle {\hat {P}}_{\text{PHD}}\left(e^{j\omega }\right)={\frac {1}{\left|\mathbf {e} ^{H}\mathbf {v} _{\text{min}}\right|^{2}}}}
1621:
1560:
532:
510:
351:
7479:
3323:
346:) are non-parametric estimators closely related to the periodogram. By contrast, the parametric approaches assume that the underlying
7511:
168:
Spectrum analysis can be performed on the entire signal. Alternatively, a signal can be broken into short segments (sometimes called
4630:
1794:
1681:
1601:
process as a regression problem and solves that problem using forward-backward method. They are competitive with the Burg estimators.
6874:
6766:
5015:
4978:
7052:
6926:
4596:
continuous and does not have a density function, and a residue, which is absolutely continuous and does have a density function.
3874:
1976:
1965:
1418:
7110:
6771:
6516:
5887:
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3118:
592:
430:
is the average of the periodograms taken of multiple segments of the signal to reduce variance of the spectral density estimate
393:
379:
6101:
7161:
6373:
6180:
6069:
6027:
4715:"New Method of Sparse Parameter Estimation in Separable Models and Its Use for Spectral Analysis of Irregularly Sampled Data"
2090:
1969:
1956:
31:
5266:
7404:
6363:
72:) of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the
45:
6413:
3574:
389:
6955:
6904:
6889:
6879:
6748:
6620:
6587:
6368:
6198:
459:
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284:
7024:
6325:
5029:
4625:
7299:
6079:
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5212:
4640:
369:
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137:) and its frequency spectrum, showing a "fundamental" frequency at 220 Hz followed by multiples (harmonics) of 220 Hz
7506:
7156:
6899:
6658:
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6544:
6452:
6163:
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5464:
5336:
445:
280:
6330:
6096:
5954:
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6405:
6259:
6188:
6108:
5966:
5947:
5655:
5376:
1670:
1644:
1023:
323:
236:
of each frequency component. These two pieces of information can be represented as a 2-dimensional vector, as a
225:
7029:
7399:
7166:
6714:
6679:
6643:
6428:
5870:
5779:
5738:
5650:
5341:
5180:
4139:
3829:
3748:
3645:
520:
468:
464:
6436:
6420:
4852:"Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares"
613:
7308:
6921:
6861:
6798:
6158:
6020:
6010:
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5774:
1677:
7069:
7006:
4050:
The variance is the covariance of the data with itself. If we now consider the same data but with a lag of
7346:
7276:
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6648:
5645:
5542:
5449:
5328:
5227:
5136:
1960:
289:
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714:
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6353:
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6042:
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5916:
5875:
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5807:
5753:
5728:
5683:
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5582:
5384:
5207:
350:
has a certain structure that can be described using a small number of parameters (for example, using an
329:
7450:
6340:
145:
The power spectral density of a segment of music is estimated by two different methods, for comparison
7294:
6869:
6818:
6794:
6756:
6674:
6653:
6605:
6484:
6462:
6431:
6217:
6168:
6086:
6059:
6015:
5971:
5733:
5509:
5389:
5128:
4863:
4726:
4677:
1617:
1516:
1099:
761:
496:
482:
427:
335:
5141:
1573:
1523:
1482:
850:
766:
7441:
7366:
7289:
6970:
6734:
6727:
6689:
6597:
6577:
6549:
6282:
6148:
6143:
6133:
6125:
5943:
5904:
5794:
5784:
5693:
5472:
5428:
5346:
5271:
5173:
3542:
3197:
1069:
297:, which is widely used for examining the frequency characteristics of noise-free functions such as
273:
7016:
279:
In practice, nearly all software and electronic devices that generate frequency spectra utilize a
7455:
7266:
7120:
6965:
6841:
6738:
6722:
6699:
6476:
6210:
6193:
6153:
6064:
5959:
5921:
5892:
5852:
5812:
5758:
5675:
5361:
5356:
5154:
4944:
4897:
4832:
4750:
4693:
4635:
1689:
1609:
607:
588:
355:
347:
4106:
3194:
Now, for simplicity, suppose the signal extends infinitely in time, so we pass to the limit as
1010:{\displaystyle Y_{t}=\phi _{1}Y_{t-1}+\phi _{2}Y_{t-2}+\cdots +\phi _{p}Y_{t-p}+\epsilon _{t},}
817:
7361:
7331:
7323:
7143:
7134:
7059:
6990:
6846:
6831:
6806:
6694:
6635:
6501:
6489:
6115:
6032:
5976:
5899:
5743:
5665:
5444:
5318:
5103:
5082:
5063:
5011:
4974:
4934:
4889:
4822:
4785:
4742:
3721:
1636:
1409:
1361:
516:
453:
433:
343:
306:
293:(FFT). The array of squared-magnitude components of a DFT is a type of power spectrum called
241:
216:
173:
121:
77:
61:
3879:
179:
7386:
7341:
7105:
7092:
6985:
6960:
6894:
6826:
6704:
6312:
6205:
6138:
6051:
5998:
5817:
5688:
5482:
5281:
5248:
5146:
4926:
4879:
4871:
4814:
4777:
4734:
4685:
4310:
1945:
1676:
If the dominant frequency changes over time, then the problem becomes the estimation of the
1660:
298:
264:
209:
153:
110:
65:
38:
4353:
4297:{\displaystyle c(\tau )=\lim _{T\to \infty }{\frac {1}{2T}}\int _{-T}^{T}x(t)x(t+\tau )dt.}
4053:
3795:
3522:
3088:
2547:
1384:
553:
7303:
7047:
6909:
6836:
6511:
6385:
6358:
6335:
6304:
5931:
5926:
5880:
5610:
5261:
4077:
3692:
1952:
1899:
1763:
1710:
1612:
approach. This involves a nonlinear optimization and is more complex than the first three.
550:
SParse
Iterative Covariance-based Estimation (SPICE) estimation, and the more generalized
421:
302:
249:
4850:
Yardibi, Tarik; Li, Jian; Stoica, Petre; Xue, Ming; Baggeroer, Arthur B. (January 2010).
2600:
2574:
539:
method useful for SDE when singular spectral features, such as sharp peaks, are expected.
80:
in the data, by observing peaks at the frequencies corresponding to these periodicities.
5132:
4867:
4730:
4681:
7252:
7247:
5710:
5640:
5286:
4575:
4555:
4535:
4408:
4388:
4333:
4164:
4144:
4030:
4024:
4002:
1928:
1739:
797:
694:
674:
253:
237:
76:
content of the signal. One purpose of estimating the spectral density is to detect any
69:
4811:
2017 IEEE International
Conference on Acoustics, Speech and Signal Processing (ICASSP)
7495:
7409:
7376:
7239:
7200:
7011:
6980:
6444:
6398:
6003:
5705:
5532:
5296:
5291:
4920:
4020:
383:
248:). A common technique in signal processing is to consider the squared amplitude, or
233:
158:
134:
5562:
4901:
4754:
4697:
338:(also called sparse) methods. The non-parametric approaches explicitly estimate the
7351:
7284:
7261:
7176:
6506:
5802:
5700:
5635:
5577:
5499:
5454:
4948:
4836:
4659:
269:
17:
5158:
4522:{\displaystyle c(\tau )=\sum _{k}{\frac {1}{2}}A_{k}^{2}\cos(2\pi \nu _{k}\tau ).}
129:
4806:
4769:
7394:
7356:
7039:
6940:
6802:
6615:
6582:
6074:
5991:
5986:
5630:
5587:
5567:
5547:
5537:
5306:
4818:
4781:
4620:
4610:
1757:
417:
294:
4851:
4714:
4552:
over the different frequencies, and is related to the distribution of power of
1951:
The most common methods for frequency estimation involve identifying the noise
606:
In parametric spectral estimation, one assumes that the signal is modeled by a
6240:
5720:
5420:
5351:
5301:
5276:
5196:
4916:
4875:
4071:
471:
that can deal with noise, incomplete data, and instrumental response functions
439:
339:
4930:
4893:
4774:
2009 IEEE International
Conference on Acoustics, Speech and Signal Processing
4746:
4738:
4689:
3307:{\displaystyle \lim _{N\to \infty }{\frac {1}{N}}\sum _{n=0}^{N-1}x_{n}^{2}.}
6393:
6245:
5865:
5660:
5572:
5557:
5552:
5517:
5150:
3509:{\displaystyle \lim _{T\to \infty }{\frac {1}{2T}}\int _{-T}^{T}x(t)^{2}dt.}
1684:. Methods for instantaneous frequency estimation include those based on the
1666:
1640:
310:
229:
228:. For perfect reconstruction, the spectrum analyzer must preserve both the
73:
4995:
Proceedings of the 37th
Meeting of the Society of Exploration Geophysicists
4805:
Sward, Johan; Adalbjornsson, Stefan Ingi; Jakobsson, Andreas (March 2017).
4023:, monotonically non-decreasing. Its jumps occur at the frequencies of the
3990:{\displaystyle S(\nu )=\sum _{k:\nu _{k}<\nu }{\frac {1}{2}}A_{k}^{2}.}
757:. The estimation problem then becomes one of estimating these parameters.
5909:
5527:
5404:
5399:
5394:
5366:
4047:, and the value of each jump is the power or variance of that component.
4884:
7414:
7115:
4770:"Missing data recovery via a nonparametric iterative adaptive approach"
4615:
361:
Following is a partial list of spectral density estimation techniques:
436:
a windowed version of
Bartlett's method that uses overlapping segments
263:
of the function, in terms of frequency instead of time; thus, it is a
172:), and spectrum analysis may be applied to these individual segments.
7336:
6317:
6291:
6271:
5522:
5313:
4807:"A generalization of the sparse iterative covariance-based estimator"
1972:(MUSIC) method, the eigenvector method, and the minimum norm method.
245:
5119:
Thomson, D. J. (1982). "Spectrum estimation and harmonic analysis".
4405:
can be decomposed into periodic components with the same periods as
527:
Estimation of signal parameters via rotational invariance techniques
760:
The most common form of parametric SDF estimate uses as a model an
1665:
If one only wants to estimate the frequency of the single loudest
1648:
1520:
are found by recursively solving the YuleâWalker equations for an
140:
128:
120:
3409:{\displaystyle x(t)=\sum _{k}A_{k}\sin(2\pi \nu _{k}t+\phi _{k})}
276:
operations can create new frequencies in the frequency spectrum.
5256:
4572:
over the frequencies: the amplitude of a frequency component of
7225:
6792:
6539:
5838:
5608:
5225:
5169:
5030:"Overview of Signal Instantaneous Frequency Estimation Methods"
4662:
and R Moses, Spectral
Analysis of Signals, Prentice Hall, 2005.
1885:{\displaystyle x(n)=\sum _{i=1}^{p}A_{i}e^{jn\omega _{i}}+w(n)}
4768:
Stoica, Petre; Li, Jian; Ling, Jun; Cheng, Yubo (April 2009).
1415:
There are a number of approaches to estimating the parameters
91:
5165:
4917:"On the resolution of the LASSO-based DOA estimation method"
410:
for which the signal samples must be evenly spaced in time (
259:
Because of reversibility, the
Fourier transform is called a
1948:
in addition to the spectral density function due to noise.
1472:{\displaystyle \phi _{1},\ldots ,\phi _{p},\sigma _{p}^{2}}
5060:
Digital
Processing of Random Signals: Theory & Methods
513:(ARMA) estimation, which generalizes the AR and MA models.
3180:{\displaystyle {\frac {1}{N}}\sum _{n=0}^{N-1}x_{n}^{2}.}
503:
th sample is correlated with noise terms in the previous
4592:
is its contribution to the average power of the signal.
1955:
to extract these components. These methods are based on
4993:
Burg, J.P. (1967) "Maximum
Entropy Spectral Analysis",
3792:
All these contributions add up to the average power of
4713:
Stoica, Petre; Babu, Prabhu; Li, Jian (January 2011).
3834:
3753:
3650:
252:; in this case the resulting plot is referred to as a
4856:
IEEE Transactions on Aerospace and Electronic Systems
4578:
4558:
4538:
4434:
4411:
4391:
4356:
4336:
4313:
4190:
4167:
4147:
4109:
4080:
4056:
4033:
4005:
3914:
3882:
3832:
3798:
3751:
3724:
3695:
3648:
3577:
3545:
3525:
3428:
3326:
3232:
3200:
3121:
3091:
2632:
2603:
2577:
2550:
2400:
2242:
2100:
1986:
1931:
1902:
1797:
1766:
1742:
1713:
1576:
1526:
1485:
1421:
1387:
1364:
1137:
1102:
1072:
1026:
887:
853:
820:
800:
769:
717:
697:
677:
616:
556:
182:
7078:
Autoregressive conditional heteroskedasticity (ARCH)
4382:
which is the average power or variance of the data.
1616:
Alternative parametric methods include fitting to a
125:
Example of voice waveform and its frequency spectrum
7385:
7322:
7275:
7238:
7193:
7175:
7142:
7133:
7091:
7038:
6999:
6948:
6939:
6860:
6817:
6747:
6713:
6667:
6634:
6596:
6563:
6475:
6384:
6303:
6258:
6226:
6179:
6124:
6050:
6041:
5851:
5793:
5767:
5719:
5674:
5621:
5508:
5463:
5437:
5419:
5375:
5327:
5247:
5238:
3635:{\displaystyle A_{k}\sin(2\pi \nu _{k}t+\phi _{k})}
5008:Statistical Digital Signal Processing and Modeling
4584:
4564:
4544:
4521:
4417:
4397:
4374:
4342:
4322:
4296:
4173:
4153:
4130:
4095:
4062:
4039:
4011:
3989:
3897:
3865:
3816:
3784:
3737:
3710:
3681:
3634:
3563:
3531:
3508:
3408:
3306:
3215:
3179:
3104:
3074:
2615:
2589:
2563:
2528:
2382:
2223:
2080:
1937:
1917:
1884:
1781:
1748:
1728:
1593:
1543:
1502:
1471:
1400:
1373:
1347:
1120:
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839:
806:
786:
749:
703:
683:
663:
574:
200:
4922:2011 International ITG Workshop on Smart Antennas
4350:exists everywhere, is finite, and is bounded by
4207:
3689:Hence, the contribution to the average power of
3430:
3234:
3112:is, for a zero-mean function as above, given by
6626:Multivariate adaptive regression splines (MARS)
4969:Percival, Donald B.; Walden, Andrew T. (1992).
4674:IEEE Transactions on Audio and Electroacoustics
4964:
4962:
4960:
4958:
4915:Panahi, Ashkan; Viberg, Mats (February 2011).
4532:This is in fact the spectral decomposition of
5181:
3826:Then the power as a function of frequency is
585:Iterative Adaptive Approach (IAA) estimation.
8:
1093:is a white noise process with zero mean and
834:
821:
610:which has a spectral density function (SDF)
4971:Spectral Analysis for Physical Applications
1059:{\displaystyle \phi _{1},\ldots ,\phi _{p}}
529:(ESPRIT) is another superresolution method.
240:, or as magnitude (amplitude) and phase in
7235:
7222:
7139:
6945:
6814:
6789:
6560:
6536:
6264:
6047:
5848:
5835:
5618:
5605:
5244:
5235:
5222:
5188:
5174:
5166:
489:th sample is correlated with the previous
157:powers, intensities) versus frequency (or
5140:
4883:
4577:
4557:
4537:
4504:
4479:
4474:
4460:
4454:
4433:
4410:
4390:
4355:
4335:
4312:
4249:
4241:
4222:
4210:
4189:
4166:
4146:
4108:
4079:
4055:
4032:
4004:
3978:
3973:
3959:
3945:
3934:
3913:
3881:
3866:{\displaystyle {\tfrac {1}{2}}A_{k}^{2},}
3854:
3849:
3833:
3831:
3797:
3785:{\displaystyle {\tfrac {1}{2}}A_{k}^{2}.}
3773:
3768:
3752:
3750:
3729:
3723:
3718:coming from the component with frequency
3694:
3682:{\displaystyle {\tfrac {1}{2}}A_{k}^{2}.}
3670:
3665:
3649:
3647:
3623:
3607:
3582:
3576:
3554:
3549:
3544:
3524:
3491:
3472:
3464:
3445:
3433:
3427:
3397:
3381:
3356:
3346:
3325:
3295:
3290:
3274:
3263:
3249:
3237:
3231:
3199:
3168:
3163:
3147:
3136:
3122:
3120:
3096:
3090:
3051:
3021:
3002:
2997:
2986:
2980:
2964:
2934:
2915:
2910:
2899:
2893:
2881:
2850:
2822:
2794:
2766:
2742:
2732:
2709:
2693:
2668:
2658:
2641:
2633:
2631:
2602:
2576:
2555:
2549:
2520:
2515:
2508:
2503:
2491:
2477:
2467:
2461:
2456:
2444:
2428:
2414:
2403:
2402:
2399:
2371:
2360:
2355:
2348:
2343:
2328:
2319:
2313:
2296:
2286:
2270:
2256:
2245:
2244:
2241:
2212:
2201:
2196:
2189:
2184:
2171:
2154:
2144:
2128:
2114:
2103:
2102:
2099:
2070:
2059:
2054:
2047:
2042:
2030:
2014:
2000:
1989:
1988:
1985:
1930:
1901:
1859:
1848:
1838:
1828:
1817:
1796:
1765:
1741:
1712:
1577:
1575:
1568:forward-backward least-squares estimators
1527:
1525:
1486:
1484:
1463:
1458:
1445:
1426:
1420:
1392:
1386:
1363:
1336:
1324:
1316:
1307:
1275:
1265:
1255:
1244:
1215:
1210:
1203:
1191:
1186:
1173:
1154:
1136:
1112:
1107:
1101:
1077:
1071:
1050:
1031:
1025:
998:
979:
969:
944:
934:
915:
905:
892:
886:
854:
852:
828:
819:
799:
770:
768:
741:
722:
716:
696:
676:
652:
633:
615:
555:
181:
4307:If it exists, it is an even function of
1756:complex exponentials in the presence of
664:{\displaystyle S(f;a_{1},\ldots ,a_{p})}
499:(MA) estimation, which assumes that the
485:(AR) estimation, which assumes that the
37:For broader coverage of this topic, see
4652:
1510:process and thus the spectral density:
352:auto-regressive or moving-average model
106:This article may need to be cleaned up.
7152:KaplanâMeier estimator (product limit)
4719:IEEE Transactions on Signal Processing
4330:If the average power is bounded, then
595:but with a sparsity enforcing penalty.
448:is a nonparametric method that uses a
399:Non-uniform discrete Fourier transform
5010:, John Wiley & Sons, Inc., 1996.
7:
7462:
7162:Accelerated failure time (AFT) model
4708:
4706:
4606:Multidimensional spectral estimation
671:that is a function of the frequency
368:for which the signal samples can be
7474:
6757:Analysis of variance (ANOVA, anova)
1622:autoregressive moving-average model
1561:maximum entropy spectral estimation
750:{\displaystyle a_{1},\ldots ,a_{p}}
533:Maximum entropy spectral estimation
467:is a nonparametric method based on
6852:CochranâMantelâHaenszel statistics
5478:Pearson product-moment correlation
4217:
3440:
3244:
3207:
1643:, amplitude, and phase-shift of a
1365:
1294:
1221:
25:
5079:Spectral Analysis and Time Series
424:of the discrete Fourier transform
7473:
7461:
7449:
7436:
7435:
3875:cumulative distribution function
2516:
2504:
2492:
2468:
2457:
2356:
2344:
2197:
2185:
2055:
2043:
1608:estimate the parameters using a
456:to estimate the spectral density
268:non-linear. For instance, only
96:
30:For the statistical method, see
7111:Least-squares spectral analysis
1381:the sampling time interval and
1315:
1121:{\displaystyle \sigma _{p}^{2}}
878:process satisfies the equation
593:least-squares spectral analysis
394:Least-squares spectral analysis
380:Least-squares spectral analysis
6092:Mean-unbiased minimum-variance
5098:Stoica, P.; Moses, R. (2005).
4973:. Cambridge University Press.
4513:
4491:
4444:
4438:
4366:
4360:
4282:
4270:
4264:
4258:
4214:
4200:
4194:
4125:
4113:
4090:
4084:
3924:
3918:
3892:
3886:
3808:
3802:
3705:
3699:
3629:
3594:
3488:
3481:
3437:
3403:
3368:
3336:
3330:
3241:
3204:
3060:
3038:
3027:
3014:
2973:
2951:
2940:
2927:
2859:
2837:
2828:
2815:
2803:
2781:
2772:
2759:
2715:
2680:
2408:
2250:
2108:
1994:
1970:multiple signal classification
1912:
1906:
1896:The power spectral density of
1879:
1873:
1807:
1801:
1776:
1770:
1723:
1717:
1594:{\displaystyle {\text{AR}}(p)}
1588:
1582:
1544:{\displaystyle {\text{AR}}(p)}
1538:
1532:
1503:{\displaystyle {\text{AR}}(p)}
1497:
1491:
1325:
1317:
1197:
1141:
1128:. The SDF for this process is
871:{\displaystyle {\text{AR}}(p)}
865:
859:
787:{\displaystyle {\text{AR}}(p)}
781:
775:
658:
620:
569:
557:
517:MUltiple SIgnal Classification
195:
189:
32:Probability density estimation
1:
7502:Statistical signal processing
7405:Geographic information system
6621:Simultaneous equations models
4631:Timeâfrequency representation
3564:{\displaystyle 1/{\sqrt {2}}}
3216:{\displaystyle N\to \infty .}
1707:A typical model for a signal
1682:timeâfrequency representation
1606:maximum likelihood estimators
1086:{\displaystyle \epsilon _{t}}
511:Autoregressive moving-average
348:stationary stochastic process
46:statistical signal processing
7517:Spectrum (physical sciences)
6588:Coefficient of determination
6199:Uniformly most powerful test
5100:Spectral Analysis of Signals
4813:. IEEE. pp. 3954â3958.
4776:. IEEE. pp. 3369â3372.
4138:, and define this to be the
460:Short-time Fourier transform
450:singular value decomposition
386:fitting to known frequencies
7157:Proportional hazards models
7101:Spectral density estimation
7083:Vector autoregression (VAR)
6517:Maximum posterior estimator
5749:Randomized controlled trial
4819:10.1109/icassp.2017.7952898
4782:10.1109/icassp.2009.4960347
4641:Spectral power distribution
1066:are fixed coefficients and
309:) or over frequency (
50:spectral density estimation
27:Signal processing technique
7533:
6917:Multivariate distributions
5337:Average absolute deviation
4997:, Oklahoma City, Oklahoma.
4131:{\displaystyle x(t+\tau )}
1658:
545:Semi-parametric techniques
446:Singular spectrum analysis
392:, an approximation of the
281:discrete Fourier transform
36:
29:
7512:Frequency-domain analysis
7431:
7234:
7221:
6905:Structural equation model
6813:
6788:
6559:
6535:
6267:
6241:Score/Lagrange multiplier
5847:
5834:
5656:Sample size determination
5617:
5604:
5234:
5221:
5203:
4876:10.1109/TAES.2010.5417172
1686:WignerâVille distribution
1671:pitch detection algorithm
840:{\displaystyle \{Y_{t}\}}
374:records can be incomplete
283:(DFT), which operates on
226:inverse Fourier transform
7400:Environmental statistics
6922:Elliptical distributions
6715:Generalized linear model
6644:Simple linear regression
6414:HodgesâLehmann estimator
5871:Probability distribution
5780:Stochastic approximation
5342:Coefficient of variation
5077:Priestley, M.B. (1991).
4931:10.1109/wsa.2011.5741938
4739:10.1109/TSP.2010.2086452
4690:10.1109/TAU.1967.1161901
4161:of the signal (or data)
4140:autocorrelation function
3738:{\displaystyle \nu _{k}}
3519:The root mean square of
1374:{\displaystyle \Delta t}
469:information field theory
412:records must be complete
390:LombâScargle periodogram
299:filter impulse responses
108:It has been merged from
7060:Cross-correlation (XCF)
6668:Non-standard predictors
6102:LehmannâScheffĂ© theorem
5775:Adaptive clinical trial
5151:10.1109/PROC.1982.12433
5121:Proceedings of the IEEE
4626:Timeâfrequency analysis
3898:{\displaystyle S(\nu )}
1678:instantaneous frequency
370:unevenly spaced in time
201:{\displaystyle \sin(t)}
7456:Mathematics portal
7277:Engineering statistics
7185:NelsonâAalen estimator
6762:Analysis of covariance
6649:Ordinary least squares
6573:Pearson product-moment
5977:Statistical functional
5888:Empirical distribution
5721:Controlled experiments
5450:Frequency distribution
5228:Descriptive statistics
5035:. University of Rijeka
4925:. IEEE. pp. 1â5.
4586:
4566:
4546:
4523:
4419:
4399:
4376:
4344:
4324:
4323:{\displaystyle \tau .}
4298:
4175:
4155:
4132:
4097:
4064:
4041:
4013:
3991:
3899:
3867:
3818:
3786:
3739:
3712:
3683:
3636:
3565:
3533:
3510:
3410:
3308:
3285:
3217:
3181:
3158:
3106:
3076:
2617:
2591:
2565:
2530:
2384:
2318:
2225:
2176:
2082:
1961:autocorrelation matrix
1939:
1919:
1886:
1833:
1783:
1750:
1730:
1595:
1545:
1517:YuleâWalker estimators
1504:
1473:
1402:
1375:
1349:
1260:
1122:
1087:
1060:
1011:
872:
841:
808:
788:
751:
705:
685:
665:
576:
547:(an incomplete list):
479:(an incomplete list):
408:Non-parametric methods
366:Non-parametric methods
290:fast Fourier transform
202:
152:, also referred to as
146:
138:
126:
70:power spectral density
7372:Population statistics
7314:System identification
7048:Autocorrelation (ACF)
6976:Exponential smoothing
6890:Discriminant analysis
6885:Canonical correlation
6749:Partition of variance
6611:Regression validation
6455:(JonckheereâTerpstra)
6354:Likelihood-ratio test
6043:Frequentist inference
5955:Locationâscale family
5876:Sampling distribution
5841:Statistical inference
5808:Cross-sectional study
5795:Observational studies
5754:Randomized experiment
5583:Stem-and-leaf display
5385:Central limit theorem
4587:
4567:
4547:
4524:
4420:
4400:
4385:It can be shown that
4377:
4375:{\displaystyle c(0),}
4345:
4325:
4299:
4176:
4156:
4133:
4098:
4065:
4063:{\displaystyle \tau }
4042:
4014:
3992:
3900:
3868:
3819:
3817:{\displaystyle x(t).}
3787:
3740:
3713:
3684:
3637:
3571:, so the variance of
3566:
3534:
3532:{\displaystyle \sin }
3511:
3411:
3309:
3259:
3218:
3182:
3132:
3107:
3105:{\displaystyle x_{n}}
3077:
2618:
2592:
2566:
2564:{\displaystyle x_{n}}
2531:
2385:
2292:
2226:
2150:
2083:
1940:
1920:
1887:
1813:
1784:
1751:
1736:consists of a sum of
1731:
1695:If one wants to know
1596:
1546:
1505:
1474:
1403:
1401:{\displaystyle f_{N}}
1376:
1350:
1240:
1123:
1088:
1061:
1012:
873:
842:
809:
789:
752:
706:
686:
666:
602:Parametric estimation
577:
575:{\displaystyle (r,q)}
519:(MUSIC) is a popular
477:Parametric techniques
356:signal reconstruction
203:
144:
133:A periodic waveform (
132:
124:
7295:Probabilistic design
6880:Principal components
6723:Exponential families
6675:Nonlinear regression
6654:General linear model
6616:Mixed effects models
6606:Errors and residuals
6583:Confounding variable
6485:Bayesian probability
6463:Van der Waerden test
6453:Ordered alternative
6218:Multiple comparisons
6097:RaoâBlackwellization
6060:Estimating equations
6016:Statistical distance
5734:Factorial experiment
5267:Arithmetic-Geometric
4676:, AU-15 (2): 70â73,
4576:
4556:
4536:
4432:
4409:
4389:
4354:
4334:
4311:
4188:
4165:
4145:
4107:
4096:{\displaystyle x(t)}
4078:
4054:
4031:
4003:
3912:
3880:
3873:and its statistical
3830:
3796:
3749:
3722:
3711:{\displaystyle x(t)}
3693:
3646:
3575:
3543:
3523:
3426:
3324:
3230:
3198:
3119:
3089:
2630:
2601:
2575:
2548:
2398:
2240:
2098:
1984:
1929:
1918:{\displaystyle x(n)}
1900:
1795:
1782:{\displaystyle w(n)}
1764:
1740:
1729:{\displaystyle x(n)}
1711:
1633:Frequency estimation
1628:Frequency estimation
1618:moving-average model
1574:
1524:
1483:
1419:
1385:
1362:
1135:
1100:
1070:
1024:
885:
851:
847:obeying a zero mean
818:
814:. A signal sequence
798:
767:
762:autoregressive model
715:
695:
675:
614:
554:
497:Moving-average model
483:Autoregressive model
180:
7367:Official statistics
7290:Methods engineering
6971:Seasonal adjustment
6739:Poisson regressions
6659:Bayesian regression
6598:Regression analysis
6578:Partial correlation
6550:Regression analysis
6149:Prediction interval
6144:Likelihood interval
6134:Confidence interval
6126:Interval estimation
6087:Unbiased estimators
5905:Model specification
5785:Up-and-down designs
5473:Partial correlation
5429:Index of dispersion
5347:Interquartile range
5133:1982IEEEP..70.1055T
4868:2010ITAES..46..425Y
4731:2011ITSP...59...35S
4682:1967ITAE...15...70W
4484:
4254:
3983:
3859:
3778:
3675:
3477:
3300:
3173:
2616:{\displaystyle N-1}
2590:{\displaystyle n=0}
2540:Example calculation
2392:Minimum norm method
1957:eigen decomposition
1690:ambiguity functions
1647:in the presence of
1620:(MA) and to a full
1468:
1220:
1196:
1117:
1095:innovation variance
68:(also known as the
58:spectral estimation
18:Spectral estimation
7387:Spatial statistics
7267:Medical statistics
7167:First hitting time
7121:Whittle likelihood
6772:Degrees of freedom
6767:Multivariate ANOVA
6700:Heteroscedasticity
6512:Bayesian estimator
6477:Bayesian inference
6326:KolmogorovâSmirnov
6211:Randomization test
6181:Testing hypotheses
6154:Tolerance interval
6065:Maximum likelihood
5960:Exponential family
5893:Density estimation
5853:Statistical theory
5813:Natural experiment
5759:Scientific control
5676:Survey methodology
5362:Standard deviation
5081:. Academic Press.
5058:Porat, B. (1994).
5006:Hayes, Monson H.,
4636:Whittle likelihood
4582:
4562:
4542:
4519:
4470:
4459:
4415:
4395:
4372:
4340:
4320:
4294:
4237:
4221:
4171:
4151:
4128:
4093:
4070:, we can take the
4060:
4037:
4009:
3987:
3969:
3958:
3895:
3863:
3845:
3843:
3814:
3782:
3764:
3762:
3735:
3708:
3679:
3661:
3659:
3632:
3561:
3529:
3506:
3460:
3444:
3406:
3351:
3304:
3286:
3248:
3213:
3177:
3159:
3102:
3072:
3070:
2886:
2737:
2663:
2613:
2587:
2561:
2526:
2380:
2234:Eigenvector method
2221:
2078:
1977:Pisarenko's method
1966:Pisarenko's method
1935:
1915:
1882:
1779:
1746:
1726:
1680:as defined in the
1635:is the process of
1610:maximum likelihood
1591:
1541:
1500:
1469:
1454:
1398:
1371:
1345:
1206:
1182:
1118:
1103:
1083:
1056:
1007:
868:
837:
804:
784:
747:
701:
681:
661:
608:stationary process
572:
334:and more recently
198:
174:Periodic functions
147:
139:
127:
7507:Signal estimation
7489:
7488:
7427:
7426:
7423:
7422:
7362:National accounts
7332:Actuarial science
7324:Social statistics
7217:
7216:
7213:
7212:
7209:
7208:
7144:Survival function
7129:
7128:
6991:Granger causality
6832:Contingency table
6807:Survival analysis
6784:
6783:
6780:
6779:
6636:Linear regression
6531:
6530:
6527:
6526:
6502:Credible interval
6471:
6470:
6254:
6253:
6070:Method of moments
5939:Parametric family
5900:Statistical model
5830:
5829:
5826:
5825:
5744:Random assignment
5666:Statistical power
5600:
5599:
5596:
5595:
5445:Contingency table
5415:
5414:
5282:Generalized/power
5109:978-0-13-113956-5
5102:. Prentice Hall.
5088:978-0-12-564922-3
5069:978-0-13-063751-2
5062:. Prentice Hall.
4940:978-1-61284-075-8
4828:978-1-5090-4117-6
4791:978-1-4244-2353-8
4585:{\displaystyle c}
4565:{\displaystyle x}
4545:{\displaystyle c}
4468:
4450:
4418:{\displaystyle x}
4398:{\displaystyle c}
4343:{\displaystyle c}
4235:
4206:
4174:{\displaystyle x}
4154:{\displaystyle c}
4040:{\displaystyle x}
4012:{\displaystyle S}
3967:
3930:
3842:
3761:
3658:
3559:
3458:
3429:
3342:
3257:
3233:
3130:
3031:
2995:
2944:
2908:
2877:
2728:
2654:
2490:
2483:
2417:
2411:
2378:
2334:
2259:
2253:
2219:
2117:
2111:
2076:
2062:
2003:
1997:
1946:impulse functions
1938:{\displaystyle p}
1749:{\displaystyle p}
1688:and higher order
1580:
1530:
1489:
1410:Nyquist frequency
1313:
857:
807:{\displaystyle p}
773:
704:{\displaystyle p}
684:{\displaystyle f}
454:covariance matrix
428:Bartlett's method
242:polar coordinates
217:Fourier transform
163:spectrum analysis
150:Spectrum analysis
119:
118:
16:(Redirected from
7524:
7477:
7476:
7465:
7464:
7454:
7453:
7439:
7438:
7342:Crime statistics
7236:
7223:
7140:
7106:Fourier analysis
7093:Frequency domain
7073:
7020:
6986:Structural break
6946:
6895:Cluster analysis
6842:Log-linear model
6815:
6790:
6731:
6705:Homoscedasticity
6561:
6537:
6456:
6448:
6440:
6439:(KruskalâWallis)
6424:
6409:
6364:Cross validation
6349:
6331:AndersonâDarling
6278:
6265:
6236:Likelihood-ratio
6228:Parametric tests
6206:Permutation test
6189:1- & 2-tails
6080:Minimum distance
6052:Point estimation
6048:
5999:Optimal decision
5950:
5849:
5836:
5818:Quasi-experiment
5768:Adaptive designs
5619:
5606:
5483:Rank correlation
5245:
5236:
5223:
5190:
5183:
5176:
5167:
5162:
5144:
5127:(9): 1055â1096.
5113:
5092:
5073:
5045:
5044:
5042:
5040:
5034:
5028:Lerga, Jonatan.
5025:
5019:
5004:
4998:
4991:
4985:
4984:
4966:
4953:
4952:
4912:
4906:
4905:
4887:
4847:
4841:
4840:
4802:
4796:
4795:
4765:
4759:
4758:
4710:
4701:
4700:
4669:
4663:
4657:
4591:
4589:
4588:
4583:
4571:
4569:
4568:
4563:
4551:
4549:
4548:
4543:
4528:
4526:
4525:
4520:
4509:
4508:
4483:
4478:
4469:
4461:
4458:
4424:
4422:
4421:
4416:
4404:
4402:
4401:
4396:
4381:
4379:
4378:
4373:
4349:
4347:
4346:
4341:
4329:
4327:
4326:
4321:
4303:
4301:
4300:
4295:
4253:
4248:
4236:
4234:
4223:
4220:
4180:
4178:
4177:
4172:
4160:
4158:
4157:
4152:
4137:
4135:
4134:
4129:
4102:
4100:
4099:
4094:
4069:
4067:
4066:
4061:
4046:
4044:
4043:
4038:
4018:
4016:
4015:
4010:
3996:
3994:
3993:
3988:
3982:
3977:
3968:
3960:
3957:
3950:
3949:
3904:
3902:
3901:
3896:
3872:
3870:
3869:
3864:
3858:
3853:
3844:
3835:
3823:
3821:
3820:
3815:
3791:
3789:
3788:
3783:
3777:
3772:
3763:
3754:
3744:
3742:
3741:
3736:
3734:
3733:
3717:
3715:
3714:
3709:
3688:
3686:
3685:
3680:
3674:
3669:
3660:
3651:
3641:
3639:
3638:
3633:
3628:
3627:
3612:
3611:
3587:
3586:
3570:
3568:
3567:
3562:
3560:
3555:
3553:
3538:
3536:
3535:
3530:
3515:
3513:
3512:
3507:
3496:
3495:
3476:
3471:
3459:
3457:
3446:
3443:
3415:
3413:
3412:
3407:
3402:
3401:
3386:
3385:
3361:
3360:
3350:
3313:
3311:
3310:
3305:
3299:
3294:
3284:
3273:
3258:
3250:
3247:
3222:
3220:
3219:
3214:
3186:
3184:
3183:
3178:
3172:
3167:
3157:
3146:
3131:
3123:
3111:
3109:
3108:
3103:
3101:
3100:
3085:The variance of
3081:
3079:
3078:
3073:
3071:
3067:
3063:
3056:
3055:
3030:
3026:
3025:
3007:
3006:
2996:
2991:
2990:
2981:
2979:
2969:
2968:
2943:
2939:
2938:
2920:
2919:
2909:
2904:
2903:
2894:
2892:
2885:
2870:
2866:
2862:
2855:
2854:
2827:
2826:
2799:
2798:
2771:
2770:
2747:
2746:
2736:
2721:
2714:
2713:
2698:
2697:
2673:
2672:
2662:
2646:
2645:
2622:
2620:
2619:
2614:
2596:
2594:
2593:
2588:
2570:
2568:
2567:
2562:
2560:
2559:
2535:
2533:
2532:
2527:
2525:
2524:
2519:
2513:
2512:
2507:
2495:
2488:
2484:
2482:
2481:
2476:
2472:
2471:
2466:
2465:
2460:
2445:
2440:
2436:
2435:
2419:
2418:
2415:
2413:
2412:
2404:
2389:
2387:
2386:
2381:
2379:
2377:
2376:
2375:
2370:
2366:
2365:
2364:
2359:
2353:
2352:
2347:
2335:
2333:
2332:
2320:
2317:
2312:
2287:
2282:
2278:
2277:
2261:
2260:
2257:
2255:
2254:
2246:
2230:
2228:
2227:
2222:
2220:
2218:
2217:
2216:
2211:
2207:
2206:
2205:
2200:
2194:
2193:
2188:
2175:
2170:
2145:
2140:
2136:
2135:
2119:
2118:
2115:
2113:
2112:
2104:
2087:
2085:
2084:
2079:
2077:
2075:
2074:
2069:
2065:
2064:
2063:
2060:
2058:
2052:
2051:
2046:
2031:
2026:
2022:
2021:
2005:
2004:
2001:
1999:
1998:
1990:
1944:
1942:
1941:
1936:
1924:
1922:
1921:
1916:
1891:
1889:
1888:
1883:
1866:
1865:
1864:
1863:
1843:
1842:
1832:
1827:
1788:
1786:
1785:
1780:
1755:
1753:
1752:
1747:
1735:
1733:
1732:
1727:
1669:, one can use a
1667:pure-tone signal
1661:Sinusoidal model
1600:
1598:
1597:
1592:
1581:
1578:
1550:
1548:
1547:
1542:
1531:
1528:
1509:
1507:
1506:
1501:
1490:
1487:
1478:
1476:
1475:
1470:
1467:
1462:
1450:
1449:
1431:
1430:
1407:
1405:
1404:
1399:
1397:
1396:
1380:
1378:
1377:
1372:
1354:
1352:
1351:
1346:
1341:
1340:
1328:
1320:
1314:
1312:
1311:
1306:
1302:
1301:
1300:
1270:
1269:
1259:
1254:
1227:
1219:
1214:
1204:
1195:
1190:
1178:
1177:
1159:
1158:
1127:
1125:
1124:
1119:
1116:
1111:
1092:
1090:
1089:
1084:
1082:
1081:
1065:
1063:
1062:
1057:
1055:
1054:
1036:
1035:
1016:
1014:
1013:
1008:
1003:
1002:
990:
989:
974:
973:
955:
954:
939:
938:
926:
925:
910:
909:
897:
896:
877:
875:
874:
869:
858:
855:
846:
844:
843:
838:
833:
832:
813:
811:
810:
805:
793:
791:
790:
785:
774:
771:
756:
754:
753:
748:
746:
745:
727:
726:
710:
708:
707:
702:
690:
688:
687:
682:
670:
668:
667:
662:
657:
656:
638:
637:
581:
579:
578:
573:
303:window functions
265:frequency domain
210:Fourier analysis
207:
205:
204:
199:
161:) can be called
154:frequency domain
111:Frequency domain
100:
99:
92:
66:spectral density
39:Spectral density
21:
7532:
7531:
7527:
7526:
7525:
7523:
7522:
7521:
7492:
7491:
7490:
7485:
7448:
7419:
7381:
7318:
7304:quality control
7271:
7253:Clinical trials
7230:
7205:
7189:
7177:Hazard function
7171:
7125:
7087:
7071:
7034:
7030:BreuschâGodfrey
7018:
6995:
6935:
6910:Factor analysis
6856:
6837:Graphical model
6809:
6776:
6743:
6729:
6709:
6663:
6630:
6592:
6555:
6554:
6523:
6467:
6454:
6446:
6438:
6422:
6407:
6386:Rank statistics
6380:
6359:Model selection
6347:
6305:Goodness of fit
6299:
6276:
6250:
6222:
6175:
6120:
6109:Median unbiased
6037:
5948:
5881:Order statistic
5843:
5822:
5789:
5763:
5715:
5670:
5613:
5611:Data collection
5592:
5504:
5459:
5433:
5411:
5371:
5323:
5240:Continuous data
5230:
5217:
5199:
5194:
5142:10.1.1.471.1278
5118:
5110:
5097:
5089:
5076:
5070:
5057:
5054:
5052:Further reading
5049:
5048:
5038:
5036:
5032:
5027:
5026:
5022:
5005:
5001:
4992:
4988:
4981:
4968:
4967:
4956:
4941:
4914:
4913:
4909:
4849:
4848:
4844:
4829:
4804:
4803:
4799:
4792:
4767:
4766:
4762:
4712:
4711:
4704:
4671:
4670:
4666:
4658:
4654:
4649:
4602:
4574:
4573:
4554:
4553:
4534:
4533:
4500:
4430:
4429:
4407:
4406:
4387:
4386:
4352:
4351:
4332:
4331:
4309:
4308:
4227:
4186:
4185:
4163:
4162:
4143:
4142:
4105:
4104:
4076:
4075:
4052:
4051:
4029:
4028:
4001:
4000:
3941:
3910:
3909:
3878:
3877:
3828:
3827:
3794:
3793:
3747:
3746:
3725:
3720:
3719:
3691:
3690:
3644:
3643:
3619:
3603:
3578:
3573:
3572:
3541:
3540:
3521:
3520:
3487:
3450:
3424:
3423:
3393:
3377:
3352:
3322:
3321:
3228:
3227:
3196:
3195:
3117:
3116:
3092:
3087:
3086:
3069:
3068:
3047:
3017:
2998:
2982:
2960:
2930:
2911:
2895:
2891:
2887:
2868:
2867:
2846:
2818:
2790:
2762:
2752:
2748:
2738:
2719:
2718:
2705:
2689:
2664:
2647:
2637:
2628:
2627:
2599:
2598:
2573:
2572:
2551:
2546:
2545:
2542:
2514:
2502:
2455:
2454:
2450:
2449:
2424:
2420:
2401:
2396:
2395:
2354:
2342:
2341:
2337:
2336:
2324:
2291:
2266:
2262:
2243:
2238:
2237:
2195:
2183:
2182:
2178:
2177:
2149:
2124:
2120:
2101:
2096:
2095:
2053:
2041:
2040:
2036:
2035:
2010:
2006:
1987:
1982:
1981:
1927:
1926:
1925:is composed of
1898:
1897:
1855:
1844:
1834:
1793:
1792:
1762:
1761:
1738:
1737:
1709:
1708:
1705:
1663:
1657:
1630:
1572:
1571:
1556:Burg estimators
1522:
1521:
1481:
1480:
1441:
1422:
1417:
1416:
1388:
1383:
1382:
1360:
1359:
1332:
1271:
1261:
1233:
1229:
1228:
1205:
1169:
1150:
1133:
1132:
1098:
1097:
1073:
1068:
1067:
1046:
1027:
1022:
1021:
994:
975:
965:
940:
930:
911:
901:
888:
883:
882:
849:
848:
824:
816:
815:
796:
795:
765:
764:
737:
718:
713:
712:
693:
692:
673:
672:
648:
629:
612:
611:
604:
552:
551:
521:superresolution
465:Critical filter
422:modulus squared
336:semi-parametric
319:
178:
177:
115:
101:
97:
90:
42:
35:
28:
23:
22:
15:
12:
11:
5:
7530:
7528:
7520:
7519:
7514:
7509:
7504:
7494:
7493:
7487:
7486:
7484:
7483:
7471:
7459:
7445:
7432:
7429:
7428:
7425:
7424:
7421:
7420:
7418:
7417:
7412:
7407:
7402:
7397:
7391:
7389:
7383:
7382:
7380:
7379:
7374:
7369:
7364:
7359:
7354:
7349:
7344:
7339:
7334:
7328:
7326:
7320:
7319:
7317:
7316:
7311:
7306:
7297:
7292:
7287:
7281:
7279:
7273:
7272:
7270:
7269:
7264:
7259:
7250:
7248:Bioinformatics
7244:
7242:
7232:
7231:
7226:
7219:
7218:
7215:
7214:
7211:
7210:
7207:
7206:
7204:
7203:
7197:
7195:
7191:
7190:
7188:
7187:
7181:
7179:
7173:
7172:
7170:
7169:
7164:
7159:
7154:
7148:
7146:
7137:
7131:
7130:
7127:
7126:
7124:
7123:
7118:
7113:
7108:
7103:
7097:
7095:
7089:
7088:
7086:
7085:
7080:
7075:
7067:
7062:
7057:
7056:
7055:
7053:partial (PACF)
7044:
7042:
7036:
7035:
7033:
7032:
7027:
7022:
7014:
7009:
7003:
7001:
7000:Specific tests
6997:
6996:
6994:
6993:
6988:
6983:
6978:
6973:
6968:
6963:
6958:
6952:
6950:
6943:
6937:
6936:
6934:
6933:
6932:
6931:
6930:
6929:
6914:
6913:
6912:
6902:
6900:Classification
6897:
6892:
6887:
6882:
6877:
6872:
6866:
6864:
6858:
6857:
6855:
6854:
6849:
6847:McNemar's test
6844:
6839:
6834:
6829:
6823:
6821:
6811:
6810:
6793:
6786:
6785:
6782:
6781:
6778:
6777:
6775:
6774:
6769:
6764:
6759:
6753:
6751:
6745:
6744:
6742:
6741:
6725:
6719:
6717:
6711:
6710:
6708:
6707:
6702:
6697:
6692:
6687:
6685:Semiparametric
6682:
6677:
6671:
6669:
6665:
6664:
6662:
6661:
6656:
6651:
6646:
6640:
6638:
6632:
6631:
6629:
6628:
6623:
6618:
6613:
6608:
6602:
6600:
6594:
6593:
6591:
6590:
6585:
6580:
6575:
6569:
6567:
6557:
6556:
6553:
6552:
6547:
6541:
6540:
6533:
6532:
6529:
6528:
6525:
6524:
6522:
6521:
6520:
6519:
6509:
6504:
6499:
6498:
6497:
6492:
6481:
6479:
6473:
6472:
6469:
6468:
6466:
6465:
6460:
6459:
6458:
6450:
6442:
6426:
6423:(MannâWhitney)
6418:
6417:
6416:
6403:
6402:
6401:
6390:
6388:
6382:
6381:
6379:
6378:
6377:
6376:
6371:
6366:
6356:
6351:
6348:(ShapiroâWilk)
6343:
6338:
6333:
6328:
6323:
6315:
6309:
6307:
6301:
6300:
6298:
6297:
6289:
6280:
6268:
6262:
6260:Specific tests
6256:
6255:
6252:
6251:
6249:
6248:
6243:
6238:
6232:
6230:
6224:
6223:
6221:
6220:
6215:
6214:
6213:
6203:
6202:
6201:
6191:
6185:
6183:
6177:
6176:
6174:
6173:
6172:
6171:
6166:
6156:
6151:
6146:
6141:
6136:
6130:
6128:
6122:
6121:
6119:
6118:
6113:
6112:
6111:
6106:
6105:
6104:
6099:
6084:
6083:
6082:
6077:
6072:
6067:
6056:
6054:
6045:
6039:
6038:
6036:
6035:
6030:
6025:
6024:
6023:
6013:
6008:
6007:
6006:
5996:
5995:
5994:
5989:
5984:
5974:
5969:
5964:
5963:
5962:
5957:
5952:
5936:
5935:
5934:
5929:
5924:
5914:
5913:
5912:
5907:
5897:
5896:
5895:
5885:
5884:
5883:
5873:
5868:
5863:
5857:
5855:
5845:
5844:
5839:
5832:
5831:
5828:
5827:
5824:
5823:
5821:
5820:
5815:
5810:
5805:
5799:
5797:
5791:
5790:
5788:
5787:
5782:
5777:
5771:
5769:
5765:
5764:
5762:
5761:
5756:
5751:
5746:
5741:
5736:
5731:
5725:
5723:
5717:
5716:
5714:
5713:
5711:Standard error
5708:
5703:
5698:
5697:
5696:
5691:
5680:
5678:
5672:
5671:
5669:
5668:
5663:
5658:
5653:
5648:
5643:
5641:Optimal design
5638:
5633:
5627:
5625:
5615:
5614:
5609:
5602:
5601:
5598:
5597:
5594:
5593:
5591:
5590:
5585:
5580:
5575:
5570:
5565:
5560:
5555:
5550:
5545:
5540:
5535:
5530:
5525:
5520:
5514:
5512:
5506:
5505:
5503:
5502:
5497:
5496:
5495:
5490:
5480:
5475:
5469:
5467:
5461:
5460:
5458:
5457:
5452:
5447:
5441:
5439:
5438:Summary tables
5435:
5434:
5432:
5431:
5425:
5423:
5417:
5416:
5413:
5412:
5410:
5409:
5408:
5407:
5402:
5397:
5387:
5381:
5379:
5373:
5372:
5370:
5369:
5364:
5359:
5354:
5349:
5344:
5339:
5333:
5331:
5325:
5324:
5322:
5321:
5316:
5311:
5310:
5309:
5304:
5299:
5294:
5289:
5284:
5279:
5274:
5272:Contraharmonic
5269:
5264:
5253:
5251:
5242:
5232:
5231:
5226:
5219:
5218:
5216:
5215:
5210:
5204:
5201:
5200:
5195:
5193:
5192:
5185:
5178:
5170:
5164:
5163:
5115:
5114:
5108:
5094:
5093:
5087:
5074:
5068:
5053:
5050:
5047:
5046:
5020:
4999:
4986:
4979:
4954:
4939:
4907:
4862:(1): 425â443.
4842:
4827:
4797:
4790:
4760:
4702:
4664:
4651:
4650:
4648:
4645:
4644:
4643:
4638:
4633:
4628:
4623:
4618:
4613:
4608:
4601:
4598:
4581:
4561:
4541:
4530:
4529:
4518:
4515:
4512:
4507:
4503:
4499:
4496:
4493:
4490:
4487:
4482:
4477:
4473:
4467:
4464:
4457:
4453:
4449:
4446:
4443:
4440:
4437:
4414:
4394:
4371:
4368:
4365:
4362:
4359:
4339:
4319:
4316:
4305:
4304:
4293:
4290:
4287:
4284:
4281:
4278:
4275:
4272:
4269:
4266:
4263:
4260:
4257:
4252:
4247:
4244:
4240:
4233:
4230:
4226:
4219:
4216:
4213:
4209:
4205:
4202:
4199:
4196:
4193:
4170:
4150:
4127:
4124:
4121:
4118:
4115:
4112:
4092:
4089:
4086:
4083:
4059:
4036:
4027:components of
4008:
3998:
3997:
3986:
3981:
3976:
3972:
3966:
3963:
3956:
3953:
3948:
3944:
3940:
3937:
3933:
3929:
3926:
3923:
3920:
3917:
3894:
3891:
3888:
3885:
3862:
3857:
3852:
3848:
3841:
3838:
3813:
3810:
3807:
3804:
3801:
3781:
3776:
3771:
3767:
3760:
3757:
3732:
3728:
3707:
3704:
3701:
3698:
3678:
3673:
3668:
3664:
3657:
3654:
3631:
3626:
3622:
3618:
3615:
3610:
3606:
3602:
3599:
3596:
3593:
3590:
3585:
3581:
3558:
3552:
3548:
3528:
3517:
3516:
3505:
3502:
3499:
3494:
3490:
3486:
3483:
3480:
3475:
3470:
3467:
3463:
3456:
3453:
3449:
3442:
3439:
3436:
3432:
3417:
3416:
3405:
3400:
3396:
3392:
3389:
3384:
3380:
3376:
3373:
3370:
3367:
3364:
3359:
3355:
3349:
3345:
3341:
3338:
3335:
3332:
3329:
3315:
3314:
3303:
3298:
3293:
3289:
3283:
3280:
3277:
3272:
3269:
3266:
3262:
3256:
3253:
3246:
3243:
3240:
3236:
3212:
3209:
3206:
3203:
3188:
3187:
3176:
3171:
3166:
3162:
3156:
3153:
3150:
3145:
3142:
3139:
3135:
3129:
3126:
3099:
3095:
3083:
3082:
3066:
3062:
3059:
3054:
3050:
3046:
3043:
3040:
3037:
3034:
3029:
3024:
3020:
3016:
3013:
3010:
3005:
3001:
2994:
2989:
2985:
2978:
2975:
2972:
2967:
2963:
2959:
2956:
2953:
2950:
2947:
2942:
2937:
2933:
2929:
2926:
2923:
2918:
2914:
2907:
2902:
2898:
2890:
2884:
2880:
2876:
2873:
2871:
2869:
2865:
2861:
2858:
2853:
2849:
2845:
2842:
2839:
2836:
2833:
2830:
2825:
2821:
2817:
2814:
2811:
2808:
2805:
2802:
2797:
2793:
2789:
2786:
2783:
2780:
2777:
2774:
2769:
2765:
2761:
2758:
2755:
2751:
2745:
2741:
2735:
2731:
2727:
2724:
2722:
2720:
2717:
2712:
2708:
2704:
2701:
2696:
2692:
2688:
2685:
2682:
2679:
2676:
2671:
2667:
2661:
2657:
2653:
2650:
2648:
2644:
2640:
2636:
2635:
2612:
2609:
2606:
2586:
2583:
2580:
2558:
2554:
2541:
2538:
2537:
2536:
2523:
2518:
2511:
2506:
2501:
2498:
2494:
2487:
2480:
2475:
2470:
2464:
2459:
2453:
2448:
2443:
2439:
2434:
2431:
2427:
2423:
2410:
2407:
2393:
2390:
2374:
2369:
2363:
2358:
2351:
2346:
2340:
2331:
2327:
2323:
2316:
2311:
2308:
2305:
2302:
2299:
2295:
2290:
2285:
2281:
2276:
2273:
2269:
2265:
2252:
2249:
2235:
2232:
2215:
2210:
2204:
2199:
2192:
2187:
2181:
2174:
2169:
2166:
2163:
2160:
2157:
2153:
2148:
2143:
2139:
2134:
2131:
2127:
2123:
2110:
2107:
2093:
2088:
2073:
2068:
2057:
2050:
2045:
2039:
2034:
2029:
2025:
2020:
2017:
2013:
2009:
1996:
1993:
1979:
1934:
1914:
1911:
1908:
1905:
1894:
1893:
1881:
1878:
1875:
1872:
1869:
1862:
1858:
1854:
1851:
1847:
1841:
1837:
1831:
1826:
1823:
1820:
1816:
1812:
1809:
1806:
1803:
1800:
1778:
1775:
1772:
1769:
1745:
1725:
1722:
1719:
1716:
1704:
1703:Multiple tones
1701:
1656:
1653:
1629:
1626:
1614:
1613:
1602:
1590:
1587:
1584:
1564:
1552:
1540:
1537:
1534:
1499:
1496:
1493:
1466:
1461:
1457:
1453:
1448:
1444:
1440:
1437:
1434:
1429:
1425:
1395:
1391:
1370:
1367:
1356:
1355:
1344:
1339:
1335:
1331:
1327:
1323:
1319:
1310:
1305:
1299:
1296:
1293:
1290:
1287:
1284:
1281:
1278:
1274:
1268:
1264:
1258:
1253:
1250:
1247:
1243:
1239:
1236:
1232:
1226:
1223:
1218:
1213:
1209:
1202:
1199:
1194:
1189:
1185:
1181:
1176:
1172:
1168:
1165:
1162:
1157:
1153:
1149:
1146:
1143:
1140:
1115:
1110:
1106:
1080:
1076:
1053:
1049:
1045:
1042:
1039:
1034:
1030:
1018:
1017:
1006:
1001:
997:
993:
988:
985:
982:
978:
972:
968:
964:
961:
958:
953:
950:
947:
943:
937:
933:
929:
924:
921:
918:
914:
908:
904:
900:
895:
891:
867:
864:
861:
836:
831:
827:
823:
803:
783:
780:
777:
744:
740:
736:
733:
730:
725:
721:
700:
680:
660:
655:
651:
647:
644:
641:
636:
632:
628:
625:
622:
619:
603:
600:
599:
598:
597:
596:
586:
583:
571:
568:
565:
562:
559:
542:
541:
540:
530:
524:
514:
508:
494:
474:
473:
472:
462:
457:
443:
437:
434:Welch's method
431:
425:
404:
403:
402:
401:
396:
387:
344:Welch's method
324:non-parametric
318:
315:
307:Welch's method
261:representation
254:power spectrum
238:complex number
197:
194:
191:
188:
185:
117:
116:
104:
102:
95:
89:
86:
48:, the goal of
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7529:
7518:
7515:
7513:
7510:
7508:
7505:
7503:
7500:
7499:
7497:
7482:
7481:
7472:
7470:
7469:
7460:
7458:
7457:
7452:
7446:
7444:
7443:
7434:
7433:
7430:
7416:
7413:
7411:
7410:Geostatistics
7408:
7406:
7403:
7401:
7398:
7396:
7393:
7392:
7390:
7388:
7384:
7378:
7377:Psychometrics
7375:
7373:
7370:
7368:
7365:
7363:
7360:
7358:
7355:
7353:
7350:
7348:
7345:
7343:
7340:
7338:
7335:
7333:
7330:
7329:
7327:
7325:
7321:
7315:
7312:
7310:
7307:
7305:
7301:
7298:
7296:
7293:
7291:
7288:
7286:
7283:
7282:
7280:
7278:
7274:
7268:
7265:
7263:
7260:
7258:
7254:
7251:
7249:
7246:
7245:
7243:
7241:
7240:Biostatistics
7237:
7233:
7229:
7224:
7220:
7202:
7201:Log-rank test
7199:
7198:
7196:
7192:
7186:
7183:
7182:
7180:
7178:
7174:
7168:
7165:
7163:
7160:
7158:
7155:
7153:
7150:
7149:
7147:
7145:
7141:
7138:
7136:
7132:
7122:
7119:
7117:
7114:
7112:
7109:
7107:
7104:
7102:
7099:
7098:
7096:
7094:
7090:
7084:
7081:
7079:
7076:
7074:
7072:(BoxâJenkins)
7068:
7066:
7063:
7061:
7058:
7054:
7051:
7050:
7049:
7046:
7045:
7043:
7041:
7037:
7031:
7028:
7026:
7025:DurbinâWatson
7023:
7021:
7015:
7013:
7010:
7008:
7007:DickeyâFuller
7005:
7004:
7002:
6998:
6992:
6989:
6987:
6984:
6982:
6981:Cointegration
6979:
6977:
6974:
6972:
6969:
6967:
6964:
6962:
6959:
6957:
6956:Decomposition
6954:
6953:
6951:
6947:
6944:
6942:
6938:
6928:
6925:
6924:
6923:
6920:
6919:
6918:
6915:
6911:
6908:
6907:
6906:
6903:
6901:
6898:
6896:
6893:
6891:
6888:
6886:
6883:
6881:
6878:
6876:
6873:
6871:
6868:
6867:
6865:
6863:
6859:
6853:
6850:
6848:
6845:
6843:
6840:
6838:
6835:
6833:
6830:
6828:
6827:Cohen's kappa
6825:
6824:
6822:
6820:
6816:
6812:
6808:
6804:
6800:
6796:
6791:
6787:
6773:
6770:
6768:
6765:
6763:
6760:
6758:
6755:
6754:
6752:
6750:
6746:
6740:
6736:
6732:
6726:
6724:
6721:
6720:
6718:
6716:
6712:
6706:
6703:
6701:
6698:
6696:
6693:
6691:
6688:
6686:
6683:
6681:
6680:Nonparametric
6678:
6676:
6673:
6672:
6670:
6666:
6660:
6657:
6655:
6652:
6650:
6647:
6645:
6642:
6641:
6639:
6637:
6633:
6627:
6624:
6622:
6619:
6617:
6614:
6612:
6609:
6607:
6604:
6603:
6601:
6599:
6595:
6589:
6586:
6584:
6581:
6579:
6576:
6574:
6571:
6570:
6568:
6566:
6562:
6558:
6551:
6548:
6546:
6543:
6542:
6538:
6534:
6518:
6515:
6514:
6513:
6510:
6508:
6505:
6503:
6500:
6496:
6493:
6491:
6488:
6487:
6486:
6483:
6482:
6480:
6478:
6474:
6464:
6461:
6457:
6451:
6449:
6443:
6441:
6435:
6434:
6433:
6430:
6429:Nonparametric
6427:
6425:
6419:
6415:
6412:
6411:
6410:
6404:
6400:
6399:Sample median
6397:
6396:
6395:
6392:
6391:
6389:
6387:
6383:
6375:
6372:
6370:
6367:
6365:
6362:
6361:
6360:
6357:
6355:
6352:
6350:
6344:
6342:
6339:
6337:
6334:
6332:
6329:
6327:
6324:
6322:
6320:
6316:
6314:
6311:
6310:
6308:
6306:
6302:
6296:
6294:
6290:
6288:
6286:
6281:
6279:
6274:
6270:
6269:
6266:
6263:
6261:
6257:
6247:
6244:
6242:
6239:
6237:
6234:
6233:
6231:
6229:
6225:
6219:
6216:
6212:
6209:
6208:
6207:
6204:
6200:
6197:
6196:
6195:
6192:
6190:
6187:
6186:
6184:
6182:
6178:
6170:
6167:
6165:
6162:
6161:
6160:
6157:
6155:
6152:
6150:
6147:
6145:
6142:
6140:
6137:
6135:
6132:
6131:
6129:
6127:
6123:
6117:
6114:
6110:
6107:
6103:
6100:
6098:
6095:
6094:
6093:
6090:
6089:
6088:
6085:
6081:
6078:
6076:
6073:
6071:
6068:
6066:
6063:
6062:
6061:
6058:
6057:
6055:
6053:
6049:
6046:
6044:
6040:
6034:
6031:
6029:
6026:
6022:
6019:
6018:
6017:
6014:
6012:
6009:
6005:
6004:loss function
6002:
6001:
6000:
5997:
5993:
5990:
5988:
5985:
5983:
5980:
5979:
5978:
5975:
5973:
5970:
5968:
5965:
5961:
5958:
5956:
5953:
5951:
5945:
5942:
5941:
5940:
5937:
5933:
5930:
5928:
5925:
5923:
5920:
5919:
5918:
5915:
5911:
5908:
5906:
5903:
5902:
5901:
5898:
5894:
5891:
5890:
5889:
5886:
5882:
5879:
5878:
5877:
5874:
5872:
5869:
5867:
5864:
5862:
5859:
5858:
5856:
5854:
5850:
5846:
5842:
5837:
5833:
5819:
5816:
5814:
5811:
5809:
5806:
5804:
5801:
5800:
5798:
5796:
5792:
5786:
5783:
5781:
5778:
5776:
5773:
5772:
5770:
5766:
5760:
5757:
5755:
5752:
5750:
5747:
5745:
5742:
5740:
5737:
5735:
5732:
5730:
5727:
5726:
5724:
5722:
5718:
5712:
5709:
5707:
5706:Questionnaire
5704:
5702:
5699:
5695:
5692:
5690:
5687:
5686:
5685:
5682:
5681:
5679:
5677:
5673:
5667:
5664:
5662:
5659:
5657:
5654:
5652:
5649:
5647:
5644:
5642:
5639:
5637:
5634:
5632:
5629:
5628:
5626:
5624:
5620:
5616:
5612:
5607:
5603:
5589:
5586:
5584:
5581:
5579:
5576:
5574:
5571:
5569:
5566:
5564:
5561:
5559:
5556:
5554:
5551:
5549:
5546:
5544:
5541:
5539:
5536:
5534:
5533:Control chart
5531:
5529:
5526:
5524:
5521:
5519:
5516:
5515:
5513:
5511:
5507:
5501:
5498:
5494:
5491:
5489:
5486:
5485:
5484:
5481:
5479:
5476:
5474:
5471:
5470:
5468:
5466:
5462:
5456:
5453:
5451:
5448:
5446:
5443:
5442:
5440:
5436:
5430:
5427:
5426:
5424:
5422:
5418:
5406:
5403:
5401:
5398:
5396:
5393:
5392:
5391:
5388:
5386:
5383:
5382:
5380:
5378:
5374:
5368:
5365:
5363:
5360:
5358:
5355:
5353:
5350:
5348:
5345:
5343:
5340:
5338:
5335:
5334:
5332:
5330:
5326:
5320:
5317:
5315:
5312:
5308:
5305:
5303:
5300:
5298:
5295:
5293:
5290:
5288:
5285:
5283:
5280:
5278:
5275:
5273:
5270:
5268:
5265:
5263:
5260:
5259:
5258:
5255:
5254:
5252:
5250:
5246:
5243:
5241:
5237:
5233:
5229:
5224:
5220:
5214:
5211:
5209:
5206:
5205:
5202:
5198:
5191:
5186:
5184:
5179:
5177:
5172:
5171:
5168:
5160:
5156:
5152:
5148:
5143:
5138:
5134:
5130:
5126:
5122:
5117:
5116:
5111:
5105:
5101:
5096:
5095:
5090:
5084:
5080:
5075:
5071:
5065:
5061:
5056:
5055:
5051:
5031:
5024:
5021:
5017:
5016:0-471-59431-8
5013:
5009:
5003:
5000:
4996:
4990:
4987:
4982:
4980:9780521435413
4976:
4972:
4965:
4963:
4961:
4959:
4955:
4950:
4946:
4942:
4936:
4932:
4928:
4924:
4923:
4918:
4911:
4908:
4903:
4899:
4895:
4891:
4886:
4881:
4877:
4873:
4869:
4865:
4861:
4857:
4853:
4846:
4843:
4838:
4834:
4830:
4824:
4820:
4816:
4812:
4808:
4801:
4798:
4793:
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4021:step function
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2105:
2094:
2092:
2089:
2071:
2066:
2048:
2037:
2032:
2027:
2023:
2018:
2015:
2011:
2007:
1991:
1980:
1978:
1975:
1974:
1973:
1971:
1967:
1962:
1958:
1954:
1949:
1947:
1932:
1909:
1903:
1876:
1870:
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590:
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406:
405:
400:
397:
395:
391:
388:
385:
384:least squares
381:
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371:
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364:
363:
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359:
357:
353:
349:
345:
341:
337:
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327:
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314:
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296:
292:
291:
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277:
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271:
266:
262:
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255:
251:
247:
243:
239:
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231:
227:
223:
218:
213:
211:
192:
186:
183:
175:
171:
166:
164:
160:
155:
151:
143:
136:
135:triangle wave
131:
123:
113:
112:
107:
103:
94:
93:
87:
85:
81:
79:
78:periodicities
75:
71:
67:
63:
59:
55:
51:
47:
40:
33:
19:
7478:
7466:
7447:
7440:
7352:Econometrics
7302: /
7285:Chemometrics
7262:Epidemiology
7255: /
7228:Applications
7100:
7070:ARIMA model
7017:Q-statistic
6966:Stationarity
6862:Multivariate
6805: /
6801: /
6799:Multivariate
6797: /
6737: /
6733: /
6507:Bayes factor
6406:Signed rank
6318:
6292:
6284:
6272:
5967:Completeness
5803:Cohort study
5701:Opinion poll
5636:Missing data
5623:Study design
5578:Scatter plot
5500:Scatter plot
5493:Spearman's Ï
5455:Grouped data
5124:
5120:
5099:
5078:
5059:
5037:. Retrieved
5023:
5007:
5002:
4994:
4989:
4970:
4921:
4910:
4885:1721.1/59588
4859:
4855:
4845:
4810:
4800:
4773:
4763:
4725:(1): 35â47.
4722:
4718:
4673:
4667:
4655:
4594:
4531:
4384:
4306:
4049:
3999:
3825:
3518:
3418:
3316:
3193:
3189:
3084:
2543:
1950:
1895:
1706:
1696:
1694:
1675:
1664:
1632:
1631:
1615:
1605:
1567:
1555:
1515:
1414:
1357:
1094:
1019:
759:
605:
544:
536:
504:
500:
490:
486:
476:
411:
407:
373:
365:
360:
328:
322:
320:
288:
278:
274:time-variant
260:
258:
244:(i.e., as a
221:
214:
169:
167:
162:
149:
148:
109:
105:
82:
57:
56:) or simply
53:
49:
43:
7480:WikiProject
7395:Cartography
7357:Jurimetrics
7309:Reliability
7040:Time domain
7019:(LjungâBox)
6941:Time-series
6819:Categorical
6803:Time-series
6795:Categorical
6730:(Bernoulli)
6565:Correlation
6545:Correlation
6341:JarqueâBera
6313:Chi-squared
6075:M-estimator
6028:Asymptotics
5972:Sufficiency
5739:Interaction
5651:Replication
5631:Effect size
5588:Violin plot
5568:Radar chart
5548:Forest plot
5538:Correlogram
5488:Kendall's Ï
4621:Spectrogram
4611:Periodogram
1758:white noise
1655:Single tone
711:parameters
418:Periodogram
382:, based on
295:periodogram
222:synthesized
7496:Categories
7347:Demography
7065:ARMA model
6870:Regression
6447:(Friedman)
6408:(Wilcoxon)
6346:Normality
6336:Lilliefors
6283:Student's
6159:Resampling
6033:Robustness
6021:divergence
6011:Efficiency
5949:(monotone)
5944:Likelihood
5861:Population
5694:Stratified
5646:Population
5465:Dependence
5421:Count data
5352:Percentile
5329:Dispersion
5262:Arithmetic
5197:Statistics
4647:References
4072:covariance
1659:See also:
1637:estimating
1570:treat the
1020:where the
440:Multitaper
340:covariance
330:parametric
317:Techniques
270:non-linear
84:spectrum.
6728:Logistic
6495:posterior
6421:Rank sum
6169:Jackknife
6164:Bootstrap
5982:Bootstrap
5917:Parameter
5866:Statistic
5661:Statistic
5573:Run chart
5558:Pie chart
5553:Histogram
5543:Fan chart
5518:Bar chart
5400:L-moments
5287:Geometric
5137:CiteSeerX
4894:0018-9251
4747:1053-587X
4511:τ
4502:ν
4498:π
4489:
4452:∑
4442:τ
4315:τ
4280:τ
4243:−
4239:∫
4218:∞
4215:→
4198:τ
4123:τ
4058:τ
3955:ν
3943:ν
3932:∑
3922:ν
3890:ν
3727:ν
3621:ϕ
3605:ν
3601:π
3592:
3466:−
3462:∫
3441:∞
3438:→
3395:ϕ
3379:ν
3375:π
3366:
3344:∑
3279:−
3261:∑
3245:∞
3242:→
3208:∞
3205:→
3152:−
3134:∑
3049:ν
3045:π
3036:
3019:ϕ
3012:
2993:⏞
2962:ν
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2932:ϕ
2925:
2906:⏞
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2820:ϕ
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2788:π
2779:
2764:ϕ
2757:
2730:∑
2707:ϕ
2691:ν
2687:π
2678:
2656:∑
2608:−
2500:λ
2433:ω
2409:^
2326:λ
2294:∑
2275:ω
2251:^
2152:∑
2133:ω
2109:^
2019:ω
1995:^
1857:ω
1815:∑
1641:frequency
1456:σ
1443:ϕ
1436:…
1424:ϕ
1366:Δ
1295:Δ
1286:π
1277:−
1263:ϕ
1242:∑
1238:−
1222:Δ
1208:σ
1184:σ
1171:ϕ
1164:…
1152:ϕ
1105:σ
1075:ϵ
1048:ϕ
1041:…
1029:ϕ
996:ϵ
984:−
967:ϕ
960:⋯
949:−
932:ϕ
920:−
903:ϕ
794:of order
732:…
643:…
537:all-poles
311:smoothing
230:amplitude
187:
176:(such as
74:frequency
7442:Category
7135:Survival
7012:Johansen
6735:Binomial
6690:Isotonic
6277:(normal)
5922:location
5729:Blocking
5684:Sampling
5563:QâQ plot
5528:Box plot
5510:Graphics
5405:Skewness
5395:Kurtosis
5367:Variance
5297:Heronian
5292:Harmonic
5039:22 March
4902:18834345
4755:15936187
4698:13900622
4660:P Stoica
4600:See also
4025:periodic
3905:will be
2544:Suppose
1953:subspace
1624:(ARMA).
507:samples.
493:samples.
224:) by an
88:Overview
62:estimate
7468:Commons
7415:Kriging
7300:Process
7257:studies
7116:Wavelet
6949:General
6116:Plug-in
5910:L space
5689:Cluster
5390:Moments
5208:Outline
5129:Bibcode
4949:7013162
4864:Bibcode
4837:5640068
4727:Bibcode
4678:Bibcode
4616:SigSpec
2571:, from
1959:of the
1551:process
1479:of the
582:-SPICE.
523:method.
452:of the
285:samples
7337:Census
6927:Normal
6875:Manova
6695:Robust
6445:2-way
6437:1-way
6275:-test
5946:
5523:Biplot
5314:Median
5307:Lehmer
5249:Center
5159:290772
5157:
5139:
5106:
5085:
5066:
5014:
4977:
4947:
4937:
4900:
4892:
4835:
4825:
4788:
4753:
4745:
4696:
2489:
1968:, the
1645:signal
535:is an
420:, the
246:phasor
170:frames
60:is to
6961:Trend
6490:prior
6432:anova
6321:-test
6295:-test
6287:-test
6194:Power
6139:Pivot
5932:shape
5927:scale
5377:Shape
5357:Range
5302:Heinz
5277:Cubic
5213:Index
5155:S2CID
5033:(PDF)
4945:S2CID
4898:S2CID
4833:S2CID
4751:S2CID
4694:S2CID
4103:with
4019:is a
2091:MUSIC
1649:noise
1358:with
589:Lasso
250:power
234:phase
159:phase
7194:Test
6394:Sign
6246:Wald
5319:Mode
5257:Mean
5104:ISBN
5083:ISBN
5064:ISBN
5041:2014
5012:ISBN
4975:ISBN
4935:ISBN
4890:ISSN
4823:ISBN
4786:ISBN
4743:ISSN
3952:<
3419:and
1639:the
1604:The
1566:The
1554:The
1514:The
1408:the
1330:<
691:and
301:and
232:and
215:The
64:the
6374:BIC
6369:AIC
5147:doi
4927:doi
4880:hdl
4872:doi
4815:doi
4778:doi
4735:doi
4686:doi
4486:cos
4208:lim
4074:of
3745:is
3642:is
3589:sin
3539:is
3527:sin
3431:lim
3363:sin
3235:lim
3033:sin
3009:cos
2946:cos
2922:sin
2832:sin
2810:cos
2776:cos
2754:sin
2675:sin
2597:to
2061:min
2002:PHD
1697:all
1673:.
414:):
272:or
184:sin
54:SDE
44:In
7498::
5153:.
5145:.
5135:.
5125:70
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4957:^
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4933:.
4919:.
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4870:.
4860:46
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4854:.
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4809:.
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4733:.
4723:59
4721:.
4717:.
4705:^
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4684:,
4425::
4181::
2416:MN
2258:EV
2116:MU
1760:,
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1529:AR
1488:AR
1412:.
856:AR
772:AR
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358:.
256:.
212:.
165:.
6319:G
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6285:t
6273:Z
5992:V
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5112:.
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5072:.
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4983:.
4951:.
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4866::
4839:.
4817::
4794:.
4780::
4757:.
4737::
4729::
4688::
4680::
4580:c
4560:x
4540:c
4517:.
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4506:k
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4318:.
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4277:+
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4204:=
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4195:(
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4120:+
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4088:t
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3936:k
3928:=
3925:)
3919:(
3916:S
3893:)
3887:(
3884:S
3861:,
3856:2
3851:k
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3840:2
3837:1
3812:.
3809:)
3806:t
3803:(
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3780:.
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3677:.
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3551:/
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3404:)
3399:k
3391:+
3388:t
3383:k
3372:2
3369:(
3358:k
3354:A
3348:k
3340:=
3337:)
3334:t
3331:(
3328:x
3302:.
3297:2
3292:n
3288:x
3282:1
3276:N
3271:0
3268:=
3265:n
3255:N
3252:1
3239:N
3211:.
3202:N
3175:.
3170:2
3165:n
3161:x
3155:1
3149:N
3144:0
3141:=
3138:n
3128:N
3125:1
3098:n
3094:x
3065:)
3061:)
3058:n
3053:k
3042:2
3039:(
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2952:(
2941:)
2936:k
2928:(
2917:k
2913:A
2901:k
2897:a
2889:(
2883:k
2875:=
2864:)
2860:)
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2829:)
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2773:)
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2703:+
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2684:2
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2660:k
2652:=
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2639:x
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2605:N
2585:0
2582:=
2579:n
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2497:=
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2362:i
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2016:j
2012:e
2008:(
1992:P
1933:p
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1811:=
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1805:n
1802:(
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1777:)
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1771:(
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1724:)
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1492:(
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1304:|
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1292:k
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1267:k
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1252:1
1249:=
1246:k
1235:1
1231:|
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1201:=
1198:)
1193:2
1188:p
1180:,
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1000:t
992:+
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977:Y
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957:+
952:2
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936:2
928:+
923:1
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913:Y
907:1
899:=
894:t
890:Y
866:)
863:p
860:(
835:}
830:t
826:Y
822:{
802:p
782:)
779:p
776:(
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570:)
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220:(
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190:(
114:.
52:(
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34:.
20:)
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