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3498:
36:
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1214:
179:
and David A. Pierce). In fact, the Ljung–Box test statistic was described explicitly in the paper that led to the use of the Box–Pierce statistic, and from which that statistic takes its name. The Box–Pierce test statistic is a simplified version of the Ljung–Box statistic for which subsequent
632:
of a fitted ARIMA model, not the original series, and in such applications the hypothesis actually being tested is that the residuals from the ARIMA model have no autocorrelation. When testing the residuals of an estimated ARIMA model, the degrees of freedom need to be adjusted to reflect the
1218:
379:
763:
240:
The data are independently distributed (i.e. the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling
556:
603:
422:
807:
495:
907:
671:
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269:
236:
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3138:
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2912:
1553:
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625:
3125:
283:
905:
Box, G. E. P.; Pierce, D. A. (1970). "Distribution of
Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models".
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1049:
1022:
1548:
1248:
1173:
687:
53:
2152:
1300:
629:
100:
2935:
2827:
119:
72:
3540:
3113:
2987:
3171:
2832:
2577:
1948:
1538:
2162:
79:
3222:
2434:
2241:
2130:
2088:
1089:
57:
1327:
3567:
3465:
2424:
828:
2474:
872:
3016:
2965:
2950:
2940:
2809:
2681:
2648:
2429:
2259:
842:
86:
3085:
2386:
882:
196:
3360:
3161:
2140:
1809:
1273:
3245:
3212:
3217:
2960:
2719:
2625:
2605:
2513:
2224:
2042:
1525:
1397:
68:
2391:
2157:
2015:
857:: the Box-Ljung statistic is included by default in output produced by the IBM SPSS Statistics Forecasting module.
511:
2977:
2745:
2466:
2320:
2249:
2169:
2027:
2008:
1716:
1437:
3090:
877:
192:
3460:
3227:
2775:
2740:
2704:
2489:
1931:
1840:
1799:
1711:
1402:
1241:
818:
614:
2497:
2481:
809:
distribution than is the distribution for the Box–Pierce statistic for all sample sizes including small ones.
564:
3369:
2982:
2922:
2859:
2219:
2081:
2071:
1921:
1835:
46:
3130:
3067:
3407:
3337:
2822:
2709:
1706:
1603:
1510:
1389:
1288:
3528:
2406:
1065:
3432:
3374:
3317:
3143:
3036:
2945:
2671:
2555:
2414:
2296:
2288:
2103:
1999:
1977:
1936:
1901:
1868:
1814:
1789:
1744:
1683:
1643:
1445:
1268:
391:
3511:
2401:
160:
at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a
3355:
2930:
2879:
2855:
2817:
2735:
2714:
2666:
2545:
2523:
2492:
2278:
2229:
2147:
2120:
2076:
2032:
1794:
1570:
1450:
774:
462:
188:
93:
3502:
3427:
3350:
3031:
2795:
2788:
2750:
2658:
2638:
2610:
2343:
2209:
2204:
2194:
2186:
2004:
1965:
1855:
1845:
1754:
1533:
1489:
1407:
1332:
1234:
975:
3516:
3327:
3181:
3026:
2902:
2799:
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2760:
2537:
2271:
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2214:
2125:
2020:
1982:
1953:
1913:
1873:
1819:
1736:
1422:
1417:
924:
498:
1113:
771:
Simulation studies have shown that the distribution for the Ljung–Box statistic is closer to a
3422:
3392:
3384:
3204:
3195:
3120:
3051:
2907:
2892:
2867:
2755:
2696:
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2550:
2176:
2093:
2037:
1960:
1804:
1726:
1505:
1379:
1193:
1187:
1169:
1148:
1045:
1039:
1018:
1014:
1163:
1142:
3447:
3402:
3166:
3153:
3046:
3021:
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2887:
2765:
2373:
2266:
2199:
2112:
2059:
1878:
1749:
1543:
1342:
1309:
1006:
987:
956:
916:
176:
161:
145:
141:
644:
435:
247:
214:
3364:
3108:
2970:
2897:
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2446:
2419:
2396:
2365:
1992:
1987:
1941:
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1322:
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502:
149:
945:
G. M. Ljung; G. E. P. Box (1978). "On a
Measure of a Lack of Fit in Time Series Models".
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1701:
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The Box–Pierce test uses the test statistic, in the notation outlined above, given by
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2459:
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1357:
1352:
1183:
1007:
1623:
3412:
3345:
3322:
3237:
2567:
1863:
1761:
1696:
1638:
1560:
1515:
920:
184:
3455:
3417:
3100:
3001:
2863:
2676:
2643:
2135:
2052:
2047:
1691:
1648:
1628:
1608:
1598:
1367:
153:
35:
2301:
1781:
1481:
1412:
1362:
1337:
1257:
991:
960:
947:
157:
17:
976:"Some power studies of a portmanteau test of time series model specification"
2454:
2306:
1926:
1721:
1633:
1618:
1613:
1578:
374:{\displaystyle Q=n(n+2)\sum _{k=1}^{h}{\frac {{\hat {\rho }}_{k}^{2}}{n-k}}}
273:
The data are not independently distributed; they exhibit serial correlation.
1970:
1588:
1465:
1460:
1455:
1427:
610:
3475:
3176:
928:
3397:
2378:
2352:
2332:
1583:
1374:
758:{\displaystyle Q_{\text{BP}}=n\sum _{k=1}^{h}{\hat {\rho }}_{k}^{2},}
1005:
Brockwell, Peter J.; Davis, Richard A.; Davis, R. J. (2002-03-08).
1317:
854:
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2600:
1899:
1669:
1286:
1230:
29:
1226:
191:. A similar assessment can be also carried out with the
1222:
768:
and it uses the same critical region as defined above.
845:: the Ljung–Box tests and the Box–Pierce tests in the
777:
690:
647:
567:
514:
465:
438:
394:
286:
250:
217:
3139:
Autoregressive conditional heteroskedasticity (ARCH)
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3383:
3336:
3299:
3254:
3236:
3203:
3194:
3152:
3099:
3060:
3009:
3000:
2921:
2878:
2808:
2774:
2728:
2695:
2657:
2624:
2536:
2445:
2364:
2319:
2287:
2240:
2185:
2111:
2102:
1912:
1854:
1828:
1780:
1735:
1682:
1569:
1524:
1498:
1480:
1436:
1388:
1308:
1299:
1168:(Third ed.). New York: Wiley. pp. 69–70.
60:. Unsourced material may be challenged and removed.
801:
757:
665:
597:
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505:for rejection of the hypothesis of randomness is:
489:
451:
416:
373:
263:
230:
641:) model, the degrees of freedom should be set to
628:(ARIMA) modeling. Note that it is applied to the
1192:. Princeton University Press. pp. 142–144.
633:parameter estimation. For example, for an ARIMA(
180:simulation studies have shown poor performance.
2687:Multivariate adaptive regression splines (MARS)
908:Journal of the American Statistical Association
1223:National Institute of Standards and Technology
1242:
8:
551:{\displaystyle Q>\chi _{1-\alpha ,h}^{2}}
156:are different from zero. Instead of testing
1144:Introduction to Time Series and Forecasting
1009:Introduction to Time Series and Forecasting
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1227:
1147:(2nd ed.). Springer. pp. 35–38.
432:is the number of lags being tested. Under
1141:Brockwell, Peter; Davis, Richard (2002).
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459:the statistic Q asymptotically follows a
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120:Learn how and when to remove this message
626:autoregressive integrated moving average
183:The Ljung–Box test is widely applied in
974:Davies, Neville; Newbold, Paul (1979).
894:
624:The Ljung–Box test is commonly used in
598:{\displaystyle \chi _{1-\alpha ,h}^{2}}
3213:Kaplan–Meier estimator (product limit)
813:Implementations in statistics packages
207:The Ljung–Box test may be defined as:
424:is the sample autocorrelation at lag
171:, and it is closely connected to the
7:
3523:
3223:Accelerated failure time (AFT) model
940:
938:
900:
898:
167:This test is sometimes known as the
58:adding citations to reliable sources
3535:
2818:Analysis of variance (ANOVA, anova)
1066:"R: Box–Pierce and Ljung–Box Tests"
2913:Cochran–Mantel–Haenszel statistics
1539:Pearson product-moment correlation
417:{\displaystyle {\hat {\rho }}_{k}}
25:
3534:
3522:
3510:
3497:
3496:
1217: This article incorporates
1212:
1013:. Taylor & Francis. p.
34:
3172:Least-squares spectral analysis
1165:Applied Econometric Time Series
802:{\displaystyle \chi _{(h)}^{2}}
490:{\displaystyle \chi _{(h)}^{2}}
45:needs additional citations for
2153:Mean-unbiased minimum-variance
921:10.1080/01621459.1970.10481180
789:
783:
735:
477:
471:
402:
341:
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1:
3563:Time series statistical tests
3466:Geographic information system
2682:Simultaneous equations models
825:function in the stats package
148:of whether any of a group of
2649:Coefficient of determination
2260:Uniformly most powerful test
3218:Proportional hazards models
3162:Spectral density estimation
3144:Vector autoregression (VAR)
2578:Maximum posterior estimator
1810:Randomized controlled trial
3584:
2978:Multivariate distributions
1398:Average absolute deviation
1044:. Blackwell. p. 162.
187:and other applications of
3492:
3295:
3282:
2966:Structural equation model
2874:
2849:
2620:
2596:
2328:
2302:Score/Lagrange multiplier
1908:
1895:
1717:Sample size determination
1678:
1665:
1295:
1282:
1264:
1090:"Python: Ljung–Box Tests"
3461:Environmental statistics
2983:Elliptical distributions
2776:Generalized linear model
2705:Simple linear regression
2475:Hodges–Lehmann estimator
1932:Probability distribution
1841:Stochastic approximation
1403:Coefficient of variation
1038:Davidson, James (2000).
873:Wald–Wolfowitz runs test
615:chi-squared distribution
3121:Cross-correlation (XCF)
2729:Non-standard predictors
2163:Lehmann–Scheffé theorem
1836:Adaptive clinical trial
1162:Enders, Walter (2010).
992:10.1093/biomet/66.1.153
961:10.1093/biomet/65.2.297
277:The test statistic is:
3517:Mathematics portal
3338:Engineering statistics
3246:Nelson–Aalen estimator
2823:Analysis of covariance
2710:Ordinary least squares
2634:Pearson product-moment
2038:Statistical functional
1949:Empirical distribution
1782:Controlled experiments
1511:Frequency distribution
1289:Descriptive statistics
1219:public domain material
803:
759:
727:
667:
605:is the (1 −
599:
552:
491:
453:
418:
375:
331:
265:
232:
175:(which is named after
3433:Population statistics
3375:System identification
3109:Autocorrelation (ACF)
3037:Exponential smoothing
2951:Discriminant analysis
2946:Canonical correlation
2810:Partition of variance
2672:Regression validation
2516:(Jonckheere–Terpstra)
2415:Likelihood-ratio test
2104:Frequentist inference
2016:Location–scale family
1937:Sampling distribution
1902:Statistical inference
1869:Cross-sectional study
1856:Observational studies
1815:Randomized experiment
1644:Stem-and-leaf display
1446:Central limit theorem
804:
760:
707:
668:
666:{\displaystyle h-p-q}
600:
553:
492:
454:
452:{\displaystyle H_{0}}
419:
376:
311:
266:
264:{\displaystyle H_{a}}
233:
231:{\displaystyle H_{0}}
3568:Time domain analysis
3356:Probabilistic design
2941:Principal components
2784:Exponential families
2736:Nonlinear regression
2715:General linear model
2677:Mixed effects models
2667:Errors and residuals
2644:Confounding variable
2546:Bayesian probability
2524:Van der Waerden test
2514:Ordered alternative
2279:Multiple comparisons
2158:Rao–Blackwellization
2121:Estimating equations
2077:Statistical distance
1795:Factorial experiment
1328:Arithmetic-Geometric
878:Breusch–Godfrey test
775:
688:
645:
621:degrees of freedom.
565:
512:
463:
436:
392:
388:is the sample size,
284:
248:
215:
193:Breusch–Godfrey test
189:time series analysis
54:improve this article
3428:Official statistics
3351:Methods engineering
3032:Seasonal adjustment
2800:Poisson regressions
2720:Bayesian regression
2659:Regression analysis
2639:Partial correlation
2611:Regression analysis
2210:Prediction interval
2205:Likelihood interval
2195:Confidence interval
2187:Interval estimation
2148:Unbiased estimators
1966:Model specification
1846:Up-and-down designs
1534:Partial correlation
1490:Index of dispersion
1408:Interquartile range
1114:"Time series tests"
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751:
594:
547:
486:
357:
3448:Spatial statistics
3328:Medical statistics
3228:First hitting time
3182:Whittle likelihood
2833:Degrees of freedom
2828:Multivariate ANOVA
2761:Heteroscedasticity
2573:Bayesian estimator
2538:Bayesian inference
2387:Kolmogorov–Smirnov
2272:Randomization test
2242:Testing hypotheses
2215:Tolerance interval
2126:Maximum likelihood
2021:Exponential family
1954:Density estimation
1914:Statistical theory
1874:Natural experiment
1820:Scientific control
1737:Survey methodology
1423:Standard deviation
1041:Econometric Theory
915:(332): 1509–1526.
883:Durbin–Watson test
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499:significance level
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197:Durbin–Watson test
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3423:National accounts
3393:Actuarial science
3385:Social statistics
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3205:Survival function
3190:
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3052:Granger causality
2893:Contingency table
2868:Survival analysis
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2697:Linear regression
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2563:Credible interval
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2131:Method of moments
2000:Parametric family
1961:Statistical model
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1805:Random assignment
1727:Statistical power
1661:
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1506:Contingency table
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1343:Generalized/power
1199:978-0-691-01018-2
1154:978-0-387-94719-8
1051:978-0-631-21584-4
1024:978-0-387-95351-9
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203:Formal definition
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16:(Redirected from
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3403:Crime statistics
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3167:Fourier analysis
3154:Frequency domain
3134:
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3047:Structural break
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2956:Cluster analysis
2903:Log-linear model
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2766:Homoscedasticity
2622:
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2500:(Kruskal–Wallis)
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2425:Cross validation
2410:
2392:Anderson–Darling
2339:
2326:
2297:Likelihood-ratio
2289:Parametric tests
2267:Permutation test
2250:1- & 2-tails
2141:Minimum distance
2113:Point estimation
2109:
2060:Optimal decision
2011:
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1879:Quasi-experiment
1829:Adaptive designs
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1544:Rank correlation
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177:George E. P. Box
169:Ljung–Box Q test
162:portmanteau test
150:autocorrelations
146:statistical test
142:George E. P. Box
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69:"Ljung–Box test"
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27:Statistical test
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3238:Hazard function
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3091:Breusch–Godfrey
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2971:Factor analysis
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2898:Graphical model
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2420:Model selection
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2366:Goodness of fit
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2170:Median unbiased
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1942:Order statistic
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3486:
3485:
3482:
3481:
3479:
3478:
3473:
3468:
3463:
3458:
3452:
3450:
3444:
3443:
3441:
3440:
3435:
3430:
3425:
3420:
3415:
3410:
3405:
3400:
3395:
3389:
3387:
3381:
3380:
3378:
3377:
3372:
3367:
3358:
3353:
3348:
3342:
3340:
3334:
3333:
3331:
3330:
3325:
3320:
3311:
3309:Bioinformatics
3305:
3303:
3293:
3292:
3287:
3280:
3279:
3276:
3275:
3272:
3271:
3268:
3267:
3265:
3264:
3258:
3256:
3252:
3251:
3249:
3248:
3242:
3240:
3234:
3233:
3231:
3230:
3225:
3220:
3215:
3209:
3207:
3198:
3192:
3191:
3188:
3187:
3185:
3184:
3179:
3174:
3169:
3164:
3158:
3156:
3150:
3149:
3147:
3146:
3141:
3136:
3128:
3123:
3118:
3117:
3116:
3114:partial (PACF)
3105:
3103:
3097:
3096:
3094:
3093:
3088:
3083:
3075:
3070:
3064:
3062:
3061:Specific tests
3058:
3057:
3055:
3054:
3049:
3044:
3039:
3034:
3029:
3024:
3019:
3013:
3011:
3004:
2998:
2997:
2995:
2994:
2993:
2992:
2991:
2990:
2975:
2974:
2973:
2963:
2961:Classification
2958:
2953:
2948:
2943:
2938:
2933:
2927:
2925:
2919:
2918:
2916:
2915:
2910:
2908:McNemar's test
2905:
2900:
2895:
2890:
2884:
2882:
2872:
2871:
2854:
2847:
2846:
2843:
2842:
2839:
2838:
2836:
2835:
2830:
2825:
2820:
2814:
2812:
2806:
2805:
2803:
2802:
2786:
2780:
2778:
2772:
2771:
2769:
2768:
2763:
2758:
2753:
2748:
2746:Semiparametric
2743:
2738:
2732:
2730:
2726:
2725:
2723:
2722:
2717:
2712:
2707:
2701:
2699:
2693:
2692:
2690:
2689:
2684:
2679:
2674:
2669:
2663:
2661:
2655:
2654:
2652:
2651:
2646:
2641:
2636:
2630:
2628:
2618:
2617:
2614:
2613:
2608:
2602:
2601:
2594:
2593:
2590:
2589:
2586:
2585:
2583:
2582:
2581:
2580:
2570:
2565:
2560:
2559:
2558:
2553:
2542:
2540:
2534:
2533:
2530:
2529:
2527:
2526:
2521:
2520:
2519:
2511:
2503:
2487:
2484:(Mann–Whitney)
2479:
2478:
2477:
2464:
2463:
2462:
2451:
2449:
2443:
2442:
2440:
2439:
2438:
2437:
2432:
2427:
2417:
2412:
2409:(Shapiro–Wilk)
2404:
2399:
2394:
2389:
2384:
2376:
2370:
2368:
2362:
2361:
2359:
2358:
2350:
2341:
2329:
2323:
2321:Specific tests
2317:
2316:
2313:
2312:
2310:
2309:
2304:
2299:
2293:
2291:
2285:
2284:
2282:
2281:
2276:
2275:
2274:
2264:
2263:
2262:
2252:
2246:
2244:
2238:
2237:
2235:
2234:
2233:
2232:
2227:
2217:
2212:
2207:
2202:
2197:
2191:
2189:
2183:
2182:
2180:
2179:
2174:
2173:
2172:
2167:
2166:
2165:
2160:
2145:
2144:
2143:
2138:
2133:
2128:
2117:
2115:
2106:
2100:
2099:
2097:
2096:
2091:
2086:
2085:
2084:
2074:
2069:
2068:
2067:
2057:
2056:
2055:
2050:
2045:
2035:
2030:
2025:
2024:
2023:
2018:
2013:
1997:
1996:
1995:
1990:
1985:
1975:
1974:
1973:
1968:
1958:
1957:
1956:
1946:
1945:
1944:
1934:
1929:
1924:
1918:
1916:
1906:
1905:
1900:
1893:
1892:
1889:
1888:
1885:
1884:
1882:
1881:
1876:
1871:
1866:
1860:
1858:
1852:
1851:
1849:
1848:
1843:
1838:
1832:
1830:
1826:
1825:
1823:
1822:
1817:
1812:
1807:
1802:
1797:
1792:
1786:
1784:
1778:
1777:
1775:
1774:
1772:Standard error
1769:
1764:
1759:
1758:
1757:
1752:
1741:
1739:
1733:
1732:
1730:
1729:
1724:
1719:
1714:
1709:
1704:
1702:Optimal design
1699:
1694:
1688:
1686:
1676:
1675:
1670:
1663:
1662:
1659:
1658:
1655:
1654:
1652:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1581:
1575:
1573:
1567:
1566:
1564:
1563:
1558:
1557:
1556:
1551:
1541:
1536:
1530:
1528:
1522:
1521:
1519:
1518:
1513:
1508:
1502:
1500:
1499:Summary tables
1496:
1495:
1493:
1492:
1486:
1484:
1478:
1477:
1474:
1473:
1471:
1470:
1469:
1468:
1463:
1458:
1448:
1442:
1440:
1434:
1433:
1431:
1430:
1425:
1420:
1415:
1410:
1405:
1400:
1394:
1392:
1386:
1385:
1383:
1382:
1377:
1372:
1371:
1370:
1365:
1360:
1355:
1350:
1345:
1340:
1335:
1333:Contraharmonic
1330:
1325:
1314:
1312:
1303:
1293:
1292:
1287:
1280:
1279:
1277:
1276:
1271:
1265:
1262:
1261:
1256:
1254:
1253:
1246:
1239:
1231:
1209:
1208:External links
1206:
1205:
1204:
1198:
1184:Hayashi, Fumio
1180:
1174:
1159:
1153:
1136:
1133:
1130:
1129:
1118:juliastats.org
1105:
1081:
1057:
1050:
1030:
1023:
997:
986:(1): 153–155.
966:
955:(2): 297–303.
934:
893:
892:
890:
887:
886:
885:
880:
875:
870:
863:
860:
859:
858:
852:
840:
833:acorr_ljungbox
826:
814:
811:
796:
791:
788:
785:
781:
766:
765:
754:
749:
744:
737:
734:
725:
720:
717:
714:
710:
706:
703:
694:
678:
675:
662:
659:
656:
653:
650:
592:
587:
584:
581:
578:
575:
571:
559:
558:
545:
540:
537:
534:
531:
528:
524:
520:
517:
484:
479:
476:
473:
469:
446:
442:
411:
404:
401:
382:
381:
367:
364:
361:
355:
350:
343:
340:
329:
324:
321:
318:
314:
310:
307:
304:
301:
298:
295:
292:
289:
275:
274:
258:
254:
242:
225:
221:
204:
201:
138:Greta M. Ljung
134:Ljung–Box test
128:
127:
42:
40:
33:
26:
24:
18:Ljung-Box test
14:
13:
10:
9:
6:
4:
3:
2:
3580:
3569:
3566:
3564:
3561:
3560:
3558:
3543:
3542:
3533:
3531:
3530:
3521:
3519:
3518:
3513:
3507:
3505:
3504:
3495:
3494:
3491:
3477:
3474:
3472:
3471:Geostatistics
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3453:
3451:
3449:
3445:
3439:
3438:Psychometrics
3436:
3434:
3431:
3429:
3426:
3424:
3421:
3419:
3416:
3414:
3411:
3409:
3406:
3404:
3401:
3399:
3396:
3394:
3391:
3390:
3388:
3386:
3382:
3376:
3373:
3371:
3368:
3366:
3362:
3359:
3357:
3354:
3352:
3349:
3347:
3344:
3343:
3341:
3339:
3335:
3329:
3326:
3324:
3321:
3319:
3315:
3312:
3310:
3307:
3306:
3304:
3302:
3301:Biostatistics
3298:
3294:
3290:
3285:
3281:
3263:
3262:Log-rank test
3260:
3259:
3257:
3253:
3247:
3244:
3243:
3241:
3239:
3235:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3210:
3208:
3206:
3202:
3199:
3197:
3193:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3159:
3157:
3155:
3151:
3145:
3142:
3140:
3137:
3135:
3133:(Box–Jenkins)
3129:
3127:
3124:
3122:
3119:
3115:
3112:
3111:
3110:
3107:
3106:
3104:
3102:
3098:
3092:
3089:
3087:
3086:Durbin–Watson
3084:
3082:
3076:
3074:
3071:
3069:
3068:Dickey–Fuller
3066:
3065:
3063:
3059:
3053:
3050:
3048:
3045:
3043:
3042:Cointegration
3040:
3038:
3035:
3033:
3030:
3028:
3025:
3023:
3020:
3018:
3017:Decomposition
3015:
3014:
3012:
3008:
3005:
3003:
2999:
2989:
2986:
2985:
2984:
2981:
2980:
2979:
2976:
2972:
2969:
2968:
2967:
2964:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2932:
2929:
2928:
2926:
2924:
2920:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2896:
2894:
2891:
2889:
2888:Cohen's kappa
2886:
2885:
2883:
2881:
2877:
2873:
2869:
2865:
2861:
2857:
2852:
2848:
2834:
2831:
2829:
2826:
2824:
2821:
2819:
2816:
2815:
2813:
2811:
2807:
2801:
2797:
2793:
2787:
2785:
2782:
2781:
2779:
2777:
2773:
2767:
2764:
2762:
2759:
2757:
2754:
2752:
2749:
2747:
2744:
2742:
2741:Nonparametric
2739:
2737:
2734:
2733:
2731:
2727:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2702:
2700:
2698:
2694:
2688:
2685:
2683:
2680:
2678:
2675:
2673:
2670:
2668:
2665:
2664:
2662:
2660:
2656:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2631:
2629:
2627:
2623:
2619:
2612:
2609:
2607:
2604:
2603:
2599:
2595:
2579:
2576:
2575:
2574:
2571:
2569:
2566:
2564:
2561:
2557:
2554:
2552:
2549:
2548:
2547:
2544:
2543:
2541:
2539:
2535:
2525:
2522:
2518:
2512:
2510:
2504:
2502:
2496:
2495:
2494:
2491:
2490:Nonparametric
2488:
2486:
2480:
2476:
2473:
2472:
2471:
2465:
2461:
2460:Sample median
2458:
2457:
2456:
2453:
2452:
2450:
2448:
2444:
2436:
2433:
2431:
2428:
2426:
2423:
2422:
2421:
2418:
2416:
2413:
2411:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2381:
2377:
2375:
2372:
2371:
2369:
2367:
2363:
2357:
2355:
2351:
2349:
2347:
2342:
2340:
2335:
2331:
2330:
2327:
2324:
2322:
2318:
2308:
2305:
2303:
2300:
2298:
2295:
2294:
2292:
2290:
2286:
2280:
2277:
2273:
2270:
2269:
2268:
2265:
2261:
2258:
2257:
2256:
2253:
2251:
2248:
2247:
2245:
2243:
2239:
2231:
2228:
2226:
2223:
2222:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2192:
2190:
2188:
2184:
2178:
2175:
2171:
2168:
2164:
2161:
2159:
2156:
2155:
2154:
2151:
2150:
2149:
2146:
2142:
2139:
2137:
2134:
2132:
2129:
2127:
2124:
2123:
2122:
2119:
2118:
2116:
2114:
2110:
2107:
2105:
2101:
2095:
2092:
2090:
2087:
2083:
2080:
2079:
2078:
2075:
2073:
2070:
2066:
2065:loss function
2063:
2062:
2061:
2058:
2054:
2051:
2049:
2046:
2044:
2041:
2040:
2039:
2036:
2034:
2031:
2029:
2026:
2022:
2019:
2017:
2014:
2012:
2006:
2003:
2002:
2001:
1998:
1994:
1991:
1989:
1986:
1984:
1981:
1980:
1979:
1976:
1972:
1969:
1967:
1964:
1963:
1962:
1959:
1955:
1952:
1951:
1950:
1947:
1943:
1940:
1939:
1938:
1935:
1933:
1930:
1928:
1925:
1923:
1920:
1919:
1917:
1915:
1911:
1907:
1903:
1898:
1894:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1861:
1859:
1857:
1853:
1847:
1844:
1842:
1839:
1837:
1834:
1833:
1831:
1827:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1787:
1785:
1783:
1779:
1773:
1770:
1768:
1767:Questionnaire
1765:
1763:
1760:
1756:
1753:
1751:
1748:
1747:
1746:
1743:
1742:
1740:
1738:
1734:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1693:
1690:
1689:
1687:
1685:
1681:
1677:
1673:
1668:
1664:
1650:
1647:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1594:Control chart
1592:
1590:
1587:
1585:
1582:
1580:
1577:
1576:
1574:
1572:
1568:
1562:
1559:
1555:
1552:
1550:
1547:
1546:
1545:
1542:
1540:
1537:
1535:
1532:
1531:
1529:
1527:
1523:
1517:
1514:
1512:
1509:
1507:
1504:
1503:
1501:
1497:
1491:
1488:
1487:
1485:
1483:
1479:
1467:
1464:
1462:
1459:
1457:
1454:
1453:
1452:
1449:
1447:
1444:
1443:
1441:
1439:
1435:
1429:
1426:
1424:
1421:
1419:
1416:
1414:
1411:
1409:
1406:
1404:
1401:
1399:
1396:
1395:
1393:
1391:
1387:
1381:
1378:
1376:
1373:
1369:
1366:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1329:
1326:
1324:
1321:
1320:
1319:
1316:
1315:
1313:
1311:
1307:
1304:
1302:
1298:
1294:
1290:
1285:
1281:
1275:
1272:
1270:
1267:
1266:
1263:
1259:
1252:
1247:
1245:
1240:
1238:
1233:
1232:
1229:
1225:
1224:
1221:from the
1220:
1207:
1201:
1195:
1191:
1190:
1185:
1181:
1177:
1171:
1167:
1166:
1160:
1156:
1150:
1146:
1145:
1139:
1138:
1134:
1119:
1115:
1109:
1106:
1095:
1091:
1085:
1082:
1071:
1067:
1061:
1058:
1053:
1047:
1043:
1042:
1034:
1031:
1026:
1020:
1016:
1011:
1010:
1001:
998:
993:
989:
985:
981:
977:
970:
967:
962:
958:
954:
950:
949:
941:
939:
935:
930:
926:
922:
918:
914:
910:
909:
901:
899:
895:
888:
884:
881:
879:
876:
874:
871:
869:
866:
865:
861:
856:
853:
850:
844:
841:
830:
827:
820:
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43:This article
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3501:
3413:Econometrics
3363: /
3346:Chemometrics
3323:Epidemiology
3316: /
3289:Applications
3131:ARIMA model
3078:Q-statistic
3077:
3027:Stationarity
2923:Multivariate
2866: /
2862: /
2860:Multivariate
2858: /
2798: /
2794: /
2568:Bayes factor
2467:Signed rank
2379:
2353:
2345:
2333:
2028:Completeness
1864:Cohort study
1762:Opinion poll
1697:Missing data
1684:Study design
1639:Scatter plot
1561:Scatter plot
1554:Spearman's ρ
1516:Grouped data
1211:
1189:Econometrics
1188:
1164:
1143:
1121:. Retrieved
1117:
1108:
1097:. Retrieved
1093:
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1073:. Retrieved
1070:stat.ethz.ch
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52:Please help
47:verification
44:
3541:WikiProject
3456:Cartography
3418:Jurimetrics
3370:Reliability
3101:Time domain
3080:(Ljung–Box)
3002:Time-series
2880:Categorical
2864:Time-series
2856:Categorical
2791:(Bernoulli)
2626:Correlation
2606:Correlation
2402:Jarque–Bera
2374:Chi-squared
2136:M-estimator
2089:Asymptotics
2033:Sufficiency
1800:Interaction
1712:Replication
1692:Effect size
1649:Violin plot
1629:Radar chart
1609:Forest plot
1599:Correlogram
1549:Kendall's τ
868:Q-statistic
837:statsmodels
154:time series
136:(named for
3557:Categories
3408:Demography
3126:ARMA model
2931:Regression
2508:(Friedman)
2469:(Wilcoxon)
2407:Normality
2397:Lilliefors
2344:Student's
2220:Resampling
2094:Robustness
2082:divergence
2072:Efficiency
2010:(monotone)
2005:Likelihood
1922:Population
1755:Stratified
1707:Population
1526:Dependence
1482:Count data
1413:Percentile
1390:Dispersion
1323:Arithmetic
1258:Statistics
1123:2020-02-04
1099:2018-07-23
1075:2016-06-05
980:Biometrika
948:Biometrika
889:References
158:randomness
80:newspapers
2789:Logistic
2556:posterior
2482:Rank sum
2230:Jackknife
2225:Bootstrap
2043:Bootstrap
1978:Parameter
1927:Statistic
1722:Statistic
1634:Run chart
1619:Pie chart
1614:Histogram
1604:Fan chart
1579:Bar chart
1461:L-moments
1348:Geometric
780:χ
736:^
733:ρ
709:∑
658:−
652:−
630:residuals
580:α
577:−
570:χ
533:α
530:−
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468:χ
403:^
400:ρ
363:−
342:^
339:ρ
313:∑
241:process).
110:June 2011
3503:Category
3196:Survival
3073:Johansen
2796:Binomial
2751:Isotonic
2338:(normal)
1983:location
1790:Blocking
1745:Sampling
1624:Q–Q plot
1589:Box plot
1571:Graphics
1466:Skewness
1456:Kurtosis
1428:Variance
1358:Heronian
1353:Harmonic
1186:(2000).
862:See also
823:Box.test
611:quantile
195:and the
3529:Commons
3476:Kriging
3361:Process
3318:studies
3177:Wavelet
3010:General
2177:Plug-in
1971:L space
1750:Cluster
1451:Moments
1269:Outline
929:2284333
851:package
839:package
613:of the
501:α, the
94:scholar
3398:Census
2988:Normal
2936:Manova
2756:Robust
2506:2-way
2498:1-way
2336:-test
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1584:Biplot
1375:Median
1368:Lehmer
1310:Center
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829:Python
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2551:prior
2493:anova
2382:-test
2356:-test
2348:-test
2255:Power
2200:Pivot
1993:shape
1988:scale
1438:Shape
1418:Range
1363:Heinz
1338:Cubic
1274:Index
925:JSTOR
843:Julia
617:with
152:of a
101:JSTOR
87:books
3255:Test
2455:Sign
2307:Wald
1380:Mode
1318:Mean
1194:ISBN
1170:ISBN
1149:ISBN
1046:ISBN
1019:ISBN
855:SPSS
519:>
140:and
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