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modeled by partial MLE is not correct. Therefore, for valid inference, the above formula for asymptotic variance should be used. For information equality to hold, one sufficient condition is that scores of the densities for each time period are uncorrelated. In dynamically complete models, the
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is available with
Poisson outcomes. For instance, one might have information on the number of patents files by a number of different firms over time. Pooled QMLE does not necessarily contain
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can, in principle, change over time even though it is often specified as static over time. Note that only the conditional mean function is specified, and we will get consistent estimates of
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as long as this mean condition is correctly specified. This leads to the following first order condition, which represents the quasi-log likelihood for the pooled
Poisson estimation:
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But, it is not assumed that the joint conditional density is correctly specified. Under some regularity conditions, partial MLE is consistent and asymptotically normal.
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McCullagh, P. and J. A. Nelder (1989): Generalized Linear Models, CRC Monographs on
Statistics and Applied Probability (Book 37), 2nd Edition, Chapman and Hall, London.
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Concretely, partial likelihood estimation uses the product of conditional densities as the density of the joint conditional distribution. This generality facilitates
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can be computationally demanding. On the other hand, allowing for misspecification generally results in violation of information equality and thus requires robust
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In the following exposition, we follow the treatment in
Wooldridge. Particularly, the asymptotic derivation is done under fixed-T, growing-N setting.
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Cameron, C. A. and P. K. Trivedi (2015) Count Panel Data, Oxford
Handbook of Panel Data, ed. by B. Baltagi, Oxford University Press, pp. 233â256
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858:), and the estimation method is mainly proposed for these purposes. The computational requirements are less stringent, especially compared to
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the starting point for
Poisson pooled QMLE is the conditional mean assumption. Specifically, we assume that for some
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is correctly specified, the above formula for asymptotic variance simplifies because information equality says
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700:{\displaystyle \max _{\theta \in \Theta }\sum _{i=1}^{N}\sum _{t=1}^{T}\log f_{t}(y_{it}\mid x_{it};\theta )}
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is correctly specified for each time period but it allows for misspecification in the conditional density of
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Wooldridge, J. (2002): Econometric
Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.
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Wooldridge, J.M., Econometric
Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.
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1208:{\displaystyle \operatorname {E} =m(x_{t},b_{0})=\mu _{t}{\text{ for }}t=1,\ldots ,T.}
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methods in panel data setting because fully specifying conditional distribution of
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The compact parameter space condition is imposed to enable the use of
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Pooled QMLE is a technique that allows estimating parameters when
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condition holds and thus simplified asymptotic variance is valid.
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In this formulation, the joint conditional density of
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Autoregressive conditional heteroskedasticity (ARCH)
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may be too technical for most readers to understand
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1501:{\displaystyle m=(x_{t},b_{0})=\exp(x_{t}b_{0})}
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3072:Multivariate adaptive regression splines (MARS)
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829:. Yet, except for special circumstances, the
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504:{\displaystyle x_{i}=(x_{i1},\dots ,x_{iT})}
433:{\displaystyle y_{i}=(y_{i1},\dots ,y_{iT})}
100:introducing citations to additional sources
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297:Partial (pooled) likelihood estimation for
111:"Partial likelihood methods for panel data"
61:Learn how and when to remove these messages
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285:Learn how and when to remove this message
267:Learn how and when to remove this message
206:Learn how and when to remove this message
190:, without removing the technical details.
817:. If the joint conditional density of y
90:Relevant discussion may be found on the
1554:
1239:
3598:KaplanâMeier estimator (product limit)
188:make it understandable to non-experts
7:
3908:
3608:Accelerated failure time (AFT) model
540:Writing the conditional density of y
244:Formatting of mathematical formulas.
3920:
3203:Analysis of variance (ANOVA, anova)
1083:, the conditional mean is given by
3298:CochranâMantelâHaenszel statistics
1924:Pearson product-moment correlation
1411:{\displaystyle \ell _{i}(b)=\sum }
1093:
593:
25:
42:This article has multiple issues.
3963:Probability distribution fitting
3919:
3907:
3895:
3882:
3881:
1245:{\displaystyle x_{t}\centerdot }
767:is correctly specified for each
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83:relies largely or entirely on a
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31:
3557:Least-squares spectral analysis
50:or discuss these issues on the
2538:Mean-unbiased minimum-variance
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838:Pooled QMLE for Poisson models
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1:
3953:Maximum likelihood estimation
3851:Geographic information system
3067:Simultaneous equations models
1079:in a compact parameter space
309:that assumes that density of
3034:Coefficient of determination
2645:Uniformly most powerful test
782:â Î that uniquely maximizes
3603:Proportional hazards models
3547:Spectral density estimation
3529:Vector autoregression (VAR)
2963:Maximum posterior estimator
2195:Randomized controlled trial
860:fixed-effect Poisson models
751: ; θ). We assume that
242:. The specific problem is:
3979:
3363:Multivariate distributions
1783:Average absolute deviation
1538:{\displaystyle x_{t}b_{0}}
789:By the usual argument for
238:to meet Knowledge (XXG)'s
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3680:
3667:
3351:Structural equation model
3259:
3234:
3005:
2981:
2713:
2687:Score/Lagrange multiplier
2293:
2280:
2102:Sample size determination
2063:
2050:
1680:
1667:
1649:
931:is specified as follows:
3846:Environmental statistics
3368:Elliptical distributions
3161:Generalized linear model
3090:Simple linear regression
2860:HodgesâLehmann estimator
2317:Probability distribution
2226:Stochastic approximation
1788:Coefficient of variation
864:unobserved heterogeneity
532:standard error estimator
303:quasi-maximum likelihood
3506:Cross-correlation (XCF)
3114:Non-standard predictors
2548:LehmannâScheffĂŠ theorem
2221:Adaptive clinical trial
1220:M-estimation techniques
3902:Mathematics portal
3723:Engineering statistics
3631:NelsonâAalen estimator
3208:Analysis of covariance
3095:Ordinary least squares
3019:Pearson product-moment
2423:Statistical functional
2334:Empirical distribution
2167:Controlled experiments
1896:Frequency distribution
1674:Descriptive statistics
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1502:
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1246:
1209:
1073:
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925:
898:
775:and that there exists
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505:
434:
363:
362:{\displaystyle x_{it}}
333:
332:{\displaystyle y_{it}}
3818:Population statistics
3760:System identification
3494:Autocorrelation (ACF)
3422:Exponential smoothing
3336:Discriminant analysis
3331:Canonical correlation
3195:Partition of variance
3057:Regression validation
2901:(JonckheereâTerpstra)
2800:Likelihood-ratio test
2489:Frequentist inference
2401:Locationâscale family
2322:Sampling distribution
2287:Statistical inference
2254:Cross-sectional study
2241:Observational studies
2200:Randomized experiment
2029:Stem-and-leaf display
1831:Central limit theorem
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1503:
1413:
1278:
1276:{\displaystyle b_{0}}
1247:
1210:
1074:
1072:{\displaystyle b_{0}}
1044:
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924:{\displaystyle x_{i}}
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897:{\displaystyle y_{i}}
850:(which can be either
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598:
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435:
364:
334:
3741:Probabilistic design
3326:Principal components
3169:Exponential families
3121:Nonlinear regression
3100:General linear model
3062:Mixed effects models
3052:Errors and residuals
3029:Confounding variable
2931:Bayesian probability
2909:Van der Waerden test
2899:Ordered alternative
2664:Multiple comparisons
2543:RaoâBlackwellization
2506:Estimating equations
2462:Statistical distance
2180:Factorial experiment
1713:Arithmetic-Geometric
1512:
1425:
1421:A popular choice is
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1090:
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938:
908:
881:
875:Poisson distribution
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249:improve this article
96:improve this article
3813:Official statistics
3736:Methods engineering
3417:Seasonal adjustment
3185:Poisson regressions
3105:Bayesian regression
3044:Regression analysis
3024:Partial correlation
2996:Regression analysis
2595:Prediction interval
2590:Likelihood interval
2580:Confidence interval
2572:Interval estimation
2533:Unbiased estimators
2351:Model specification
2231:Up-and-down designs
1919:Partial correlation
1875:Index of dispersion
1793:Interquartile range
1020:
3833:Spatial statistics
3713:Medical statistics
3613:First hitting time
3567:Whittle likelihood
3218:Degrees of freedom
3213:Multivariate ANOVA
3146:Heteroscedasticity
2958:Bayesian estimator
2923:Bayesian inference
2772:KolmogorovâSmirnov
2657:Randomization test
2627:Testing hypotheses
2600:Tolerance interval
2511:Maximum likelihood
2406:Exponential family
2339:Density estimation
2299:Statistical theory
2259:Natural experiment
2205:Scientific control
2122:Survey methodology
1808:Standard deviation
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848:unobserved effects
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18:Partial likelihood
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3808:National accounts
3778:Actuarial science
3770:Social statistics
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3590:Survival function
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3437:Granger causality
3278:Contingency table
3253:Survival analysis
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3082:Linear regression
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2948:Credible interval
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2516:Method of moments
2385:Parametric family
2346:Statistical model
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2190:Random assignment
2112:Statistical power
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240:quality standards
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3539:Frequency domain
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3432:Structural break
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3341:Cluster analysis
3288:Log-linear model
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3151:Homoscedasticity
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2885:(KruskalâWallis)
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2810:Cross validation
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2777:AndersonâDarling
2724:
2711:
2682:Likelihood-ratio
2674:Parametric tests
2652:Permutation test
2635:1- & 2-tails
2526:Minimum distance
2498:Point estimation
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2445:Optimal decision
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2264:Quasi-experiment
2214:Adaptive designs
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3750:quality control
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3699:Clinical trials
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3623:Hazard function
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3476:BreuschâGodfrey
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3356:Factor analysis
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3283:Graphical model
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2832:Rank statistics
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2805:Model selection
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2751:Goodness of fit
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2555:Median unbiased
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2327:Order statistic
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2057:Data collection
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1879:
1857:
1817:
1769:
1686:Continuous data
1676:
1663:
1645:
1640:
1610:
1609:
1604:
1600:
1595:
1588:
1583:
1572:
1567:
1556:
1551:
1525:
1515:
1510:
1509:
1485:
1475:
1450:
1437:
1423:
1422:
1383:
1349:
1321:
1293:
1288:
1287:
1263:
1258:
1257:
1252:. The function
1229:
1224:
1223:
1178: for
1166:
1150:
1137:
1115:
1102:
1088:
1087:
1059:
1054:
1053:
1023:
1022:
1009:
987:
979:
978:
960:
947:
936:
935:
911:
906:
905:
884:
879:
878:
840:
824:
820:
810:
806:
796:
794:
780:
764:
760:
756:
749:
742:
735:
729:
722:
715:
675:
659:
646:
577:
576:
570:
563:
556:
549:
543:
534:for inference.
528:
517:
485:
463:
447:
442:
441:
414:
392:
376:
371:
370:
346:
341:
340:
316:
311:
310:
291:
280:
279:
278:
273:
262:
256:
253:
246:
227:
223:
212:
201:
195:
192:
184:help improve it
181:
172:
168:
157:
151:
148:
105:
103:
89:
77:
36:
32:
23:
22:
15:
12:
11:
5:
3976:
3974:
3966:
3965:
3960:
3955:
3950:
3940:
3939:
3933:
3932:
3930:
3929:
3917:
3905:
3891:
3878:
3875:
3874:
3871:
3870:
3867:
3866:
3864:
3863:
3858:
3853:
3848:
3843:
3837:
3835:
3829:
3828:
3826:
3825:
3820:
3815:
3810:
3805:
3800:
3795:
3790:
3785:
3780:
3774:
3772:
3766:
3765:
3763:
3762:
3757:
3752:
3743:
3738:
3733:
3727:
3725:
3719:
3718:
3716:
3715:
3710:
3705:
3696:
3694:Bioinformatics
3690:
3688:
3678:
3677:
3672:
3665:
3664:
3661:
3660:
3657:
3656:
3653:
3652:
3650:
3649:
3643:
3641:
3637:
3636:
3634:
3633:
3627:
3625:
3619:
3618:
3616:
3615:
3610:
3605:
3600:
3594:
3592:
3583:
3577:
3576:
3573:
3572:
3570:
3569:
3564:
3559:
3554:
3549:
3543:
3541:
3535:
3534:
3532:
3531:
3526:
3521:
3513:
3508:
3503:
3502:
3501:
3499:partial (PACF)
3490:
3488:
3482:
3481:
3479:
3478:
3473:
3468:
3460:
3455:
3449:
3447:
3446:Specific tests
3443:
3442:
3440:
3439:
3434:
3429:
3424:
3419:
3414:
3409:
3404:
3398:
3396:
3389:
3383:
3382:
3380:
3379:
3378:
3377:
3376:
3375:
3360:
3359:
3358:
3348:
3346:Classification
3343:
3338:
3333:
3328:
3323:
3318:
3312:
3310:
3304:
3303:
3301:
3300:
3295:
3293:McNemar's test
3290:
3285:
3280:
3275:
3269:
3267:
3257:
3256:
3239:
3232:
3231:
3228:
3227:
3224:
3223:
3221:
3220:
3215:
3210:
3205:
3199:
3197:
3191:
3190:
3188:
3187:
3171:
3165:
3163:
3157:
3156:
3154:
3153:
3148:
3143:
3138:
3133:
3131:Semiparametric
3128:
3123:
3117:
3115:
3111:
3110:
3108:
3107:
3102:
3097:
3092:
3086:
3084:
3078:
3077:
3075:
3074:
3069:
3064:
3059:
3054:
3048:
3046:
3040:
3039:
3037:
3036:
3031:
3026:
3021:
3015:
3013:
3003:
3002:
2999:
2998:
2993:
2987:
2986:
2979:
2978:
2975:
2974:
2971:
2970:
2968:
2967:
2966:
2965:
2955:
2950:
2945:
2944:
2943:
2938:
2927:
2925:
2919:
2918:
2915:
2914:
2912:
2911:
2906:
2905:
2904:
2896:
2888:
2872:
2869:(MannâWhitney)
2864:
2863:
2862:
2849:
2848:
2847:
2836:
2834:
2828:
2827:
2825:
2824:
2823:
2822:
2817:
2812:
2802:
2797:
2794:(ShapiroâWilk)
2789:
2784:
2779:
2774:
2769:
2761:
2755:
2753:
2747:
2746:
2744:
2743:
2735:
2726:
2714:
2708:
2706:Specific tests
2702:
2701:
2698:
2697:
2695:
2694:
2689:
2684:
2678:
2676:
2670:
2669:
2667:
2666:
2661:
2660:
2659:
2649:
2648:
2647:
2637:
2631:
2629:
2623:
2622:
2620:
2619:
2618:
2617:
2612:
2602:
2597:
2592:
2587:
2582:
2576:
2574:
2568:
2567:
2565:
2564:
2559:
2558:
2557:
2552:
2551:
2550:
2545:
2530:
2529:
2528:
2523:
2518:
2513:
2502:
2500:
2491:
2485:
2484:
2482:
2481:
2476:
2471:
2470:
2469:
2459:
2454:
2453:
2452:
2442:
2441:
2440:
2435:
2430:
2420:
2415:
2410:
2409:
2408:
2403:
2398:
2382:
2381:
2380:
2375:
2370:
2360:
2359:
2358:
2353:
2343:
2342:
2341:
2331:
2330:
2329:
2319:
2314:
2309:
2303:
2301:
2291:
2290:
2285:
2278:
2277:
2274:
2273:
2270:
2269:
2267:
2266:
2261:
2256:
2251:
2245:
2243:
2237:
2236:
2234:
2233:
2228:
2223:
2217:
2215:
2211:
2210:
2208:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2171:
2169:
2163:
2162:
2160:
2159:
2157:Standard error
2154:
2149:
2144:
2143:
2142:
2137:
2126:
2124:
2118:
2117:
2115:
2114:
2109:
2104:
2099:
2094:
2089:
2087:Optimal design
2084:
2079:
2073:
2071:
2061:
2060:
2055:
2048:
2047:
2044:
2043:
2040:
2039:
2037:
2036:
2031:
2026:
2021:
2016:
2011:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1971:
1966:
1960:
1958:
1952:
1951:
1949:
1948:
1943:
1942:
1941:
1936:
1926:
1921:
1915:
1913:
1907:
1906:
1904:
1903:
1898:
1893:
1887:
1885:
1884:Summary tables
1881:
1880:
1878:
1877:
1871:
1869:
1863:
1862:
1859:
1858:
1856:
1855:
1854:
1853:
1848:
1843:
1833:
1827:
1825:
1819:
1818:
1816:
1815:
1810:
1805:
1800:
1795:
1790:
1785:
1779:
1777:
1771:
1770:
1768:
1767:
1762:
1757:
1756:
1755:
1750:
1745:
1740:
1735:
1730:
1725:
1720:
1718:Contraharmonic
1715:
1710:
1699:
1697:
1688:
1678:
1677:
1672:
1665:
1664:
1662:
1661:
1656:
1650:
1647:
1646:
1641:
1639:
1638:
1631:
1624:
1616:
1608:
1607:
1598:
1586:
1570:
1553:
1552:
1550:
1547:
1532:
1528:
1522:
1518:
1497:
1492:
1488:
1482:
1478:
1474:
1471:
1468:
1465:
1462:
1457:
1453:
1449:
1444:
1440:
1436:
1433:
1430:
1419:
1418:
1407:
1404:
1401:
1398:
1393:
1390:
1386:
1382:
1379:
1376:
1373:
1370:
1367:
1364:
1359:
1356:
1352:
1348:
1345:
1342:
1339:
1336:
1331:
1328:
1324:
1320:
1317:
1314:
1311:
1308:
1305:
1300:
1296:
1270:
1266:
1241:
1236:
1232:
1216:
1215:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1173:
1169:
1165:
1162:
1157:
1153:
1149:
1144:
1140:
1136:
1133:
1130:
1127:
1122:
1118:
1114:
1109:
1105:
1101:
1098:
1095:
1066:
1062:
1050:
1049:
1035:
1030:
1026:
1016:
1012:
1006:
1002:
994:
990:
986:
982:
975:
972:
967:
963:
959:
954:
950:
946:
943:
918:
914:
891:
887:
852:random effects
839:
836:
822:
818:
808:
804:
778:
762:
758:
754:
747:
740:
733:
727:
724:is modeled as
720:
713:
708:
707:
696:
693:
690:
685:
682:
678:
674:
669:
666:
662:
658:
653:
649:
645:
642:
637:
632:
629:
626:
622:
616:
611:
608:
605:
601:
595:
592:
589:
585:
568:
561:
554:
547:
541:
526:
516:
513:
500:
495:
492:
488:
484:
481:
478:
473:
470:
466:
462:
459:
454:
450:
429:
424:
421:
417:
413:
410:
407:
402:
399:
395:
391:
388:
383:
379:
356:
353:
349:
326:
323:
319:
307:panel analysis
293:
292:
275:
274:
230:
228:
221:
214:
213:
175:
173:
166:
159:
158:
94:. Please help
80:
78:
71:
66:
40:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3975:
3964:
3961:
3959:
3956:
3954:
3951:
3949:
3946:
3945:
3943:
3928:
3927:
3918:
3916:
3915:
3906:
3904:
3903:
3898:
3892:
3890:
3889:
3880:
3879:
3876:
3862:
3859:
3857:
3856:Geostatistics
3854:
3852:
3849:
3847:
3844:
3842:
3839:
3838:
3836:
3834:
3830:
3824:
3823:Psychometrics
3821:
3819:
3816:
3814:
3811:
3809:
3806:
3804:
3801:
3799:
3796:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3775:
3773:
3771:
3767:
3761:
3758:
3756:
3753:
3751:
3747:
3744:
3742:
3739:
3737:
3734:
3732:
3729:
3728:
3726:
3724:
3720:
3714:
3711:
3709:
3706:
3704:
3700:
3697:
3695:
3692:
3691:
3689:
3687:
3686:Biostatistics
3683:
3679:
3675:
3670:
3666:
3648:
3647:Log-rank test
3645:
3644:
3642:
3638:
3632:
3629:
3628:
3626:
3624:
3620:
3614:
3611:
3609:
3606:
3604:
3601:
3599:
3596:
3595:
3593:
3591:
3587:
3584:
3582:
3578:
3568:
3565:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3544:
3542:
3540:
3536:
3530:
3527:
3525:
3522:
3520:
3518:(BoxâJenkins)
3514:
3512:
3509:
3507:
3504:
3500:
3497:
3496:
3495:
3492:
3491:
3489:
3487:
3483:
3477:
3474:
3472:
3471:DurbinâWatson
3469:
3467:
3461:
3459:
3456:
3454:
3453:DickeyâFuller
3451:
3450:
3448:
3444:
3438:
3435:
3433:
3430:
3428:
3427:Cointegration
3425:
3423:
3420:
3418:
3415:
3413:
3410:
3408:
3405:
3403:
3402:Decomposition
3400:
3399:
3397:
3393:
3390:
3388:
3384:
3374:
3371:
3370:
3369:
3366:
3365:
3364:
3361:
3357:
3354:
3353:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3317:
3314:
3313:
3311:
3309:
3305:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3273:Cohen's kappa
3271:
3270:
3268:
3266:
3262:
3258:
3254:
3250:
3246:
3242:
3237:
3233:
3219:
3216:
3214:
3211:
3209:
3206:
3204:
3201:
3200:
3198:
3196:
3192:
3186:
3182:
3178:
3172:
3170:
3167:
3166:
3164:
3162:
3158:
3152:
3149:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3126:Nonparametric
3124:
3122:
3119:
3118:
3116:
3112:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3087:
3085:
3083:
3079:
3073:
3070:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3049:
3047:
3045:
3041:
3035:
3032:
3030:
3027:
3025:
3022:
3020:
3017:
3016:
3014:
3012:
3008:
3004:
2997:
2994:
2992:
2989:
2988:
2984:
2980:
2964:
2961:
2960:
2959:
2956:
2954:
2951:
2949:
2946:
2942:
2939:
2937:
2934:
2933:
2932:
2929:
2928:
2926:
2924:
2920:
2910:
2907:
2903:
2897:
2895:
2889:
2887:
2881:
2880:
2879:
2876:
2875:Nonparametric
2873:
2871:
2865:
2861:
2858:
2857:
2856:
2850:
2846:
2845:Sample median
2843:
2842:
2841:
2838:
2837:
2835:
2833:
2829:
2821:
2818:
2816:
2813:
2811:
2808:
2807:
2806:
2803:
2801:
2798:
2796:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2766:
2762:
2760:
2757:
2756:
2754:
2752:
2748:
2742:
2740:
2736:
2734:
2732:
2727:
2725:
2720:
2716:
2715:
2712:
2709:
2707:
2703:
2693:
2690:
2688:
2685:
2683:
2680:
2679:
2677:
2675:
2671:
2665:
2662:
2658:
2655:
2654:
2653:
2650:
2646:
2643:
2642:
2641:
2638:
2636:
2633:
2632:
2630:
2628:
2624:
2616:
2613:
2611:
2608:
2607:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2577:
2575:
2573:
2569:
2563:
2560:
2556:
2553:
2549:
2546:
2544:
2541:
2540:
2539:
2536:
2535:
2534:
2531:
2527:
2524:
2522:
2519:
2517:
2514:
2512:
2509:
2508:
2507:
2504:
2503:
2501:
2499:
2495:
2492:
2490:
2486:
2480:
2477:
2475:
2472:
2468:
2465:
2464:
2463:
2460:
2458:
2455:
2451:
2450:loss function
2448:
2447:
2446:
2443:
2439:
2436:
2434:
2431:
2429:
2426:
2425:
2424:
2421:
2419:
2416:
2414:
2411:
2407:
2404:
2402:
2399:
2397:
2391:
2388:
2387:
2386:
2383:
2379:
2376:
2374:
2371:
2369:
2366:
2365:
2364:
2361:
2357:
2354:
2352:
2349:
2348:
2347:
2344:
2340:
2337:
2336:
2335:
2332:
2328:
2325:
2324:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2304:
2302:
2300:
2296:
2292:
2288:
2283:
2279:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2246:
2244:
2242:
2238:
2232:
2229:
2227:
2224:
2222:
2219:
2218:
2216:
2212:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2172:
2170:
2168:
2164:
2158:
2155:
2153:
2152:Questionnaire
2150:
2148:
2145:
2141:
2138:
2136:
2133:
2132:
2131:
2128:
2127:
2125:
2123:
2119:
2113:
2110:
2108:
2105:
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856:fixed effects
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831:joint density
828:
816:
815:A = E and B=E
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176:This article
174:
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164:
155:
152:November 2015
144:
141:
137:
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127:
123:
120:
116:
113: â
112:
108:
107:Find sources:
101:
97:
93:
87:
86:
85:single source
81:This article
79:
75:
70:
69:
64:
62:
55:
54:
49:
48:
43:
38:
29:
28:
19:
3948:M-estimators
3924:
3912:
3893:
3886:
3798:Econometrics
3748: /
3731:Chemometrics
3708:Epidemiology
3701: /
3674:Applications
3516:ARIMA model
3463:Q-statistic
3412:Stationarity
3308:Multivariate
3251: /
3247: /
3245:Multivariate
3243: /
3183: /
3179: /
2953:Bayes factor
2852:Signed rank
2764:
2738:
2730:
2718:
2413:Completeness
2249:Cohort study
2147:Opinion poll
2082:Missing data
2069:Study design
2024:Scatter plot
1946:Scatter plot
1939:Spearman's Ď
1901:Grouped data
1601:
1420:
1253:
1217:
1080:
1051:
872:
867:
841:
826:
814:
802:
797:
791:M-estimators
788:
783:
776:
772:
768:
752:
745:
738:
731:
725:
718:
711:
709:
566:
559:
552:
545:
539:
536:
524:
518:
296:
281:
263:
254:
247:Please help
243:
232:
202:
193:
177:
149:
139:
132:
125:
118:
106:
82:
58:
51:
45:
44:Please help
41:
3926:WikiProject
3841:Cartography
3803:Jurimetrics
3755:Reliability
3486:Time domain
3465:(LjungâBox)
3387:Time-series
3265:Categorical
3249:Time-series
3241:Categorical
3176:(Bernoulli)
3011:Correlation
2991:Correlation
2787:JarqueâBera
2759:Chi-squared
2521:M-estimator
2474:Asymptotics
2418:Sufficiency
2185:Interaction
2097:Replication
2077:Effect size
2034:Violin plot
2014:Radar chart
1994:Forest plot
1984:Correlogram
1934:Kendall's Ď
515:Description
305:method for
251:if you can.
3958:Panel data
3942:Categories
3793:Demography
3511:ARMA model
3316:Regression
2893:(Friedman)
2854:(Wilcoxon)
2792:Normality
2782:Lilliefors
2729:Student's
2605:Resampling
2479:Robustness
2467:divergence
2457:Efficiency
2395:(monotone)
2390:Likelihood
2307:Population
2140:Stratified
2092:Population
1911:Dependence
1867:Count data
1798:Percentile
1775:Dispersion
1708:Arithmetic
1643:Statistics
1549:References
844:panel data
811:) is A BA
765: ; θ)
299:panel data
257:March 2018
196:April 2018
122:newspapers
47:improve it
3174:Logistic
2941:posterior
2867:Rank sum
2615:Jackknife
2610:Bootstrap
2428:Bootstrap
2363:Parameter
2312:Statistic
2107:Statistic
2019:Run chart
2004:Pie chart
1999:Histogram
1989:Fan chart
1964:Bar chart
1846:L-moments
1733:Geometric
1470:
1375:−
1338:
1316:∑
1295:ℓ
1240:⋅
1194:…
1168:μ
1113:∣
1097:
1001:μ
989:μ
985:−
958:∣
692:θ
673:∣
644:
621:∑
600:∑
594:Θ
591:∈
588:θ
480:…
409:…
92:talk page
53:talk page
3888:Category
3581:Survival
3458:Johansen
3181:Binomial
3136:Isotonic
2723:(normal)
2368:location
2175:Blocking
2130:Sampling
2009:QâQ plot
1974:Box plot
1956:Graphics
1851:Skewness
1841:Kurtosis
1813:Variance
1743:Heronian
1738:Harmonic
771:= 1,...,
233:require
3914:Commons
3861:Kriging
3746:Process
3703:studies
3562:Wavelet
3395:General
2562:Plug-in
2356:L space
2135:Cluster
1836:Moments
1654:Outline
821:given x
795:√
235:cleanup
182:Please
136:scholar
3783:Census
3373:Normal
3321:Manova
3141:Robust
2891:2-way
2883:1-way
2721:-test
2392:
1969:Biplot
1760:Median
1753:Lehmer
1695:Center
904:given
813:where
717:given
544:given
440:given
339:given
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131:
124:
117:
109:
3407:Trend
2936:prior
2878:anova
2767:-test
2741:-test
2733:-test
2640:Power
2585:Pivot
2378:shape
2373:scale
1823:Shape
1803:Range
1748:Heinz
1723:Cubic
1659:Index
301:is a
143:JSTOR
129:books
3640:Test
2840:Sign
2692:Wald
1765:Mode
1703:Mean
873:The
784:E.
115:news
2820:BIC
2815:AIC
1467:exp
1335:log
877:of
854:or
827:B=A
807:- θ
805:MLE
641:log
584:max
551:as
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