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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
694:
1211:, while the conditional mean reflects the fact that the population mean of a Poisson process is the parameter of interest. In this particular case, the parameter governing the Poisson process is allowed to vary with respect to the vector
1202:
1036:
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835:
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
1245:
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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1239:
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775:
But, it is not assumed that the joint conditional density is correctly specified. Under some regularity conditions, partial MLE is consistent and asymptotically normal.
1594:
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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110:
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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
3007:
41:
847:), and the estimation method is mainly proposed for these purposes. The computational requirements are less stringent, especially compared to
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1497:, as Poisson processes are defined over the positive real line. This reduces the conditional moment to an exponential index function, where
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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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689:{\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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1197:{\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
1031:{\displaystyle f(y_{i}\mid x_{i})={\frac {e^{-\mu _{i}}\mu _{i}^{y_{i}}}{y_{i}!}}}
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The compact parameter space condition is imposed to enable the use of
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855:. Pooled refers to pooling the data over the different time periods
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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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1957:
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859:, while QMLE refers to the quasi-maximum likelihood technique.
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851:, but the trade off is the possibly strong assumption of no
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In this formulation, the joint conditional density of
561:;θ), the partial maximum likelihood estimator solves:
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782:(details in Wooldridge ), the asymptotic variance 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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1534:is the linear index and exp is the link function.
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1490:{\displaystyle m=(x_{t},b_{0})=\exp(x_{t}b_{0})}
572:
3061:Multivariate adaptive regression splines (MARS)
1616:
1576:
1560:
818:. Yet, except for special circumstances, the
493:{\displaystyle x_{i}=(x_{i1},\dots ,x_{iT})}
422:{\displaystyle y_{i}=(y_{i1},\dots ,y_{iT})}
89:introducing citations to additional sources
1553:
1551:
1549:
1547:
286:Partial (pooled) likelihood estimation for
100:"Partial likelihood methods for panel data"
50:Learn how and when to remove these messages
1661:
1623:
1609:
2274:
274:Learn how and when to remove this message
256:Learn how and when to remove this message
195:Learn how and when to remove this message
179:, without removing the technical details.
1544:
806:. If the joint conditional density of y
79:Relevant discussion may be found on the
3929:
3587:KaplanâMeier estimator (product limit)
3660:
3227:
2974:
2273:
2043:
1660:
1604:
177:make it understandable to non-experts
3897:
3597:Accelerated failure time (AFT) model
529:Writing the conditional density of y
233:Formatting of mathematical formulas.
206:
151:
56:
15:
3909:
3192:Analysis of variance (ANOVA, anova)
2044:
1072:, the conditional mean is given by
13:
3287:CochranâMantelâHaenszel statistics
1913:Pearson product-moment correlation
1400:{\displaystyle \ell _{i}(b)=\sum }
1082:
582:
14:
3963:
1228:
31:This article has multiple issues.
3952:Probability distribution fitting
3908:
3896:
3884:
3871:
3870:
3661:
1234:{\displaystyle x_{t}\centerdot }
756:is correctly specified for each
211:
156:
72:relies largely or entirely on a
61:
20:
3546:Least-squares spectral analysis
39:or discuss these issues on the
2527:Mean-unbiased minimum-variance
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1588:
1484:
1461:
1449:
1423:
1394:
1391:
1369:
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1335:
1329:
1307:
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1123:
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1088:
959:
933:
827:Pooled QMLE for Poisson models
683:
645:
503:
487:
449:
416:
378:
1:
3942:Maximum likelihood estimation
3840:Geographic information system
3056:Simultaneous equations models
1537:
1068:in a compact parameter space
298:that assumes that density of
3023:Coefficient of determination
2634:Uniformly most powerful test
771:â Î that uniquely maximizes
7:
3592:Proportional hazards models
3536:Spectral density estimation
3518:Vector autoregression (VAR)
2952:Maximum posterior estimator
2184:Randomized controlled trial
849:fixed-effect Poisson models
740: ; θ). We assume that
231:. The specific problem is:
10:
3968:
3352:Multivariate distributions
1772:Average absolute deviation
1527:{\displaystyle x_{t}b_{0}}
778:By the usual argument for
3866:
3820:
3757:
3710:
3673:
3669:
3656:
3628:
3610:
3577:
3568:
3526:
3473:
3434:
3383:
3374:
3340:Structural equation model
3295:
3252:
3248:
3223:
3182:
3148:
3102:
3069:
3031:
2998:
2994:
2970:
2910:
2819:
2738:
2702:
2693:
2676:Score/Lagrange multiplier
2661:
2614:
2559:
2485:
2476:
2286:
2282:
2269:
2228:
2202:
2154:
2109:
2091:Sample size determination
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2052:
2039:
1943:
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1872:
1854:
1810:
1762:
1682:
1673:
1669:
1656:
1638:
920:is specified as follows:
3835:Environmental statistics
3357:Elliptical distributions
3150:Generalized linear model
3079:Simple linear regression
2849:HodgesâLehmann estimator
2306:Probability distribution
2215:Stochastic approximation
1777:Coefficient of variation
853:unobserved heterogeneity
521:standard error estimator
292:quasi-maximum likelihood
3495:Cross-correlation (XCF)
3103:Non-standard predictors
2537:LehmannâScheffĂŠ theorem
2210:Adaptive clinical trial
1209:M-estimation techniques
3891:Mathematics portal
3712:Engineering statistics
3620:NelsonâAalen estimator
3197:Analysis of covariance
3084:Ordinary least squares
3008:Pearson product-moment
2412:Statistical functional
2323:Empirical distribution
2156:Controlled experiments
1885:Frequency distribution
1663:Descriptive statistics
1528:
1491:
1401:
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1235:
1198:
1062:
1032:
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887:
764:and that there exists
690:
628:
607:
494:
423:
352:
351:{\displaystyle x_{it}}
322:
321:{\displaystyle y_{it}}
3807:Population statistics
3749:System identification
3483:Autocorrelation (ACF)
3411:Exponential smoothing
3325:Discriminant analysis
3320:Canonical correlation
3184:Partition of variance
3046:Regression validation
2890:(JonckheereâTerpstra)
2789:Likelihood-ratio test
2478:Frequentist inference
2390:Locationâscale family
2311:Sampling distribution
2276:Statistical inference
2243:Cross-sectional study
2230:Observational studies
2189:Randomized experiment
2018:Stem-and-leaf display
1820:Central limit theorem
1529:
1492:
1402:
1267:
1265:{\displaystyle b_{0}}
1236:
1199:
1063:
1061:{\displaystyle b_{0}}
1033:
915:
913:{\displaystyle x_{i}}
888:
886:{\displaystyle y_{i}}
839:(which can be either
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608:
587:
495:
424:
353:
323:
3730:Probabilistic design
3315:Principal components
3158:Exponential families
3110:Nonlinear regression
3089:General linear model
3051:Mixed effects models
3041:Errors and residuals
3018:Confounding variable
2920:Bayesian probability
2898:Van der Waerden test
2888:Ordered alternative
2653:Multiple comparisons
2532:RaoâBlackwellization
2495:Estimating equations
2451:Statistical distance
2169:Factorial experiment
1702:Arithmetic-Geometric
1501:
1414:
1410:A popular choice is
1279:
1249:
1215:
1079:
1045:
927:
897:
870:
864:Poisson distribution
568:
433:
362:
332:
302:
238:improve this article
227:to meet Knowledge's
85:improve this article
3802:Official statistics
3725:Methods engineering
3406:Seasonal adjustment
3174:Poisson regressions
3094:Bayesian regression
3033:Regression analysis
3013:Partial correlation
2985:Regression analysis
2584:Prediction interval
2579:Likelihood interval
2569:Confidence interval
2561:Interval estimation
2522:Unbiased estimators
2340:Model specification
2220:Up-and-down designs
1908:Partial correlation
1864:Index of dispersion
1782:Interquartile range
1009:
3822:Spatial statistics
3702:Medical statistics
3602:First hitting time
3556:Whittle likelihood
3207:Degrees of freedom
3202:Multivariate ANOVA
3135:Heteroscedasticity
2947:Bayesian estimator
2912:Bayesian inference
2761:KolmogorovâSmirnov
2646:Randomization test
2616:Testing hypotheses
2589:Tolerance interval
2500:Maximum likelihood
2395:Exponential family
2328:Density estimation
2288:Statistical theory
2248:Natural experiment
2194:Scientific control
2111:Survey methodology
1797:Standard deviation
1524:
1487:
1397:
1262:
1231:
1194:
1058:
1028:
988:
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837:unobserved effects
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510:maximum likelihood
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3797:National accounts
3767:Actuarial science
3759:Social statistics
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3579:Survival function
3564:
3563:
3426:Granger causality
3267:Contingency table
3242:Survival analysis
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3218:
3215:
3214:
3071:Linear regression
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2965:
2962:
2961:
2937:Credible interval
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2905:
2689:
2688:
2505:Method of moments
2374:Parametric family
2335:Statistical model
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2260:
2179:Random assignment
2101:Statistical power
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2034:
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1880:Contingency table
1850:
1849:
1717:Generalized/power
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571:
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229:quality standards
220:This article may
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3777:Crime statistics
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3541:Fourier analysis
3528:Frequency domain
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3455:
3421:Structural break
3381:
3380:
3330:Cluster analysis
3277:Log-linear model
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3140:Homoscedasticity
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2891:
2883:
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2874:(KruskalâWallis)
2859:
2844:
2799:Cross validation
2784:
2766:AndersonâDarling
2713:
2700:
2699:
2671:Likelihood-ratio
2663:Parametric tests
2641:Permutation test
2624:1- & 2-tails
2515:Minimum distance
2487:Point estimation
2483:
2482:
2434:Optimal decision
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2284:
2283:
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2253:Quasi-experiment
2203:Adaptive designs
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1918:Rank correlation
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3854:
3816:
3753:
3739:quality control
3706:
3688:Clinical trials
3665:
3640:
3624:
3612:Hazard function
3606:
3560:
3522:
3506:
3469:
3465:BreuschâGodfrey
3453:
3430:
3370:
3345:Factor analysis
3291:
3272:Graphical model
3244:
3211:
3178:
3164:
3144:
3098:
3065:
3027:
2990:
2989:
2958:
2902:
2889:
2881:
2873:
2857:
2842:
2821:Rank statistics
2815:
2794:Model selection
2782:
2740:Goodness of fit
2734:
2711:
2685:
2657:
2610:
2555:
2544:Median unbiased
2472:
2383:
2316:Order statistic
2278:
2257:
2224:
2198:
2150:
2105:
2048:
2046:Data collection
2027:
1939:
1894:
1868:
1846:
1806:
1758:
1675:Continuous data
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1338:
1314:
1310:
1286:
1282:
1280:
1277:
1276:
1256:
1252:
1250:
1247:
1246:
1241:. The function
1222:
1218:
1216:
1213:
1212:
1167: for
1165:
1159:
1155:
1143:
1139:
1130:
1126:
1108:
1104:
1095:
1091:
1080:
1077:
1076:
1052:
1048:
1046:
1043:
1042:
1016:
1012:
1011:
1002:
998:
997:
992:
980:
976:
972:
968:
967:
965:
953:
949:
940:
936:
928:
925:
924:
904:
900:
898:
895:
894:
877:
873:
871:
868:
867:
829:
813:
809:
799:
795:
785:
783:
769:
753:
749:
745:
738:
731:
724:
718:
711:
704:
668:
664:
652:
648:
639:
635:
623:
612:
602:
591:
575:
569:
566:
565:
559:
552:
545:
538:
532:
523:for inference.
517:
506:
478:
474:
456:
452:
440:
436:
434:
431:
430:
407:
403:
385:
381:
369:
365:
363:
360:
359:
339:
335:
333:
330:
329:
309:
305:
303:
300:
299:
280:
269:
268:
267:
262:
251:
245:
242:
235:
216:
212:
201:
190:
184:
181:
173:help improve it
170:
161:
157:
146:
140:
137:
94:
92:
78:
66:
25:
21:
12:
11:
5:
3965:
3955:
3954:
3949:
3944:
3939:
3922:
3921:
3919:
3918:
3906:
3894:
3880:
3867:
3864:
3863:
3860:
3859:
3856:
3855:
3853:
3852:
3847:
3842:
3837:
3832:
3826:
3824:
3818:
3817:
3815:
3814:
3809:
3804:
3799:
3794:
3789:
3784:
3779:
3774:
3769:
3763:
3761:
3755:
3754:
3752:
3751:
3746:
3741:
3732:
3727:
3722:
3716:
3714:
3708:
3707:
3705:
3704:
3699:
3694:
3685:
3683:Bioinformatics
3679:
3677:
3667:
3666:
3654:
3653:
3650:
3649:
3646:
3645:
3642:
3641:
3639:
3638:
3632:
3630:
3626:
3625:
3623:
3622:
3616:
3614:
3608:
3607:
3605:
3604:
3599:
3594:
3589:
3583:
3581:
3572:
3566:
3565:
3562:
3561:
3559:
3558:
3553:
3548:
3543:
3538:
3532:
3530:
3524:
3523:
3521:
3520:
3515:
3510:
3502:
3497:
3492:
3491:
3490:
3488:partial (PACF)
3479:
3477:
3471:
3470:
3468:
3467:
3462:
3457:
3449:
3444:
3438:
3436:
3435:Specific tests
3432:
3431:
3429:
3428:
3423:
3418:
3413:
3408:
3403:
3398:
3393:
3387:
3385:
3378:
3372:
3371:
3369:
3368:
3367:
3366:
3365:
3364:
3349:
3348:
3347:
3337:
3335:Classification
3332:
3327:
3322:
3317:
3312:
3307:
3301:
3299:
3293:
3292:
3290:
3289:
3284:
3282:McNemar's test
3279:
3274:
3269:
3264:
3258:
3256:
3246:
3245:
3221:
3220:
3217:
3216:
3213:
3212:
3210:
3209:
3204:
3199:
3194:
3188:
3186:
3180:
3179:
3177:
3176:
3160:
3154:
3152:
3146:
3145:
3143:
3142:
3137:
3132:
3127:
3122:
3120:Semiparametric
3117:
3112:
3106:
3104:
3100:
3099:
3097:
3096:
3091:
3086:
3081:
3075:
3073:
3067:
3066:
3064:
3063:
3058:
3053:
3048:
3043:
3037:
3035:
3029:
3028:
3026:
3025:
3020:
3015:
3010:
3004:
3002:
2992:
2991:
2988:
2987:
2982:
2976:
2968:
2967:
2964:
2963:
2960:
2959:
2957:
2956:
2955:
2954:
2944:
2939:
2934:
2933:
2932:
2927:
2916:
2914:
2908:
2907:
2904:
2903:
2901:
2900:
2895:
2894:
2893:
2885:
2877:
2861:
2858:(MannâWhitney)
2853:
2852:
2851:
2838:
2837:
2836:
2825:
2823:
2817:
2816:
2814:
2813:
2812:
2811:
2806:
2801:
2791:
2786:
2783:(ShapiroâWilk)
2778:
2773:
2768:
2763:
2758:
2750:
2744:
2742:
2736:
2735:
2733:
2732:
2724:
2715:
2703:
2697:
2695:Specific tests
2691:
2690:
2687:
2686:
2684:
2683:
2678:
2673:
2667:
2665:
2659:
2658:
2656:
2655:
2650:
2649:
2648:
2638:
2637:
2636:
2626:
2620:
2618:
2612:
2611:
2609:
2608:
2607:
2606:
2601:
2591:
2586:
2581:
2576:
2571:
2565:
2563:
2557:
2556:
2554:
2553:
2548:
2547:
2546:
2541:
2540:
2539:
2534:
2519:
2518:
2517:
2512:
2507:
2502:
2491:
2489:
2480:
2474:
2473:
2471:
2470:
2465:
2460:
2459:
2458:
2448:
2443:
2442:
2441:
2431:
2430:
2429:
2424:
2419:
2409:
2404:
2399:
2398:
2397:
2392:
2387:
2371:
2370:
2369:
2364:
2359:
2349:
2348:
2347:
2342:
2332:
2331:
2330:
2320:
2319:
2318:
2308:
2303:
2298:
2292:
2290:
2280:
2279:
2267:
2266:
2263:
2262:
2259:
2258:
2256:
2255:
2250:
2245:
2240:
2234:
2232:
2226:
2225:
2223:
2222:
2217:
2212:
2206:
2204:
2200:
2199:
2197:
2196:
2191:
2186:
2181:
2176:
2171:
2166:
2160:
2158:
2152:
2151:
2149:
2148:
2146:Standard error
2143:
2138:
2133:
2132:
2131:
2126:
2115:
2113:
2107:
2106:
2104:
2103:
2098:
2093:
2088:
2083:
2078:
2076:Optimal design
2073:
2068:
2062:
2060:
2050:
2049:
2037:
2036:
2033:
2032:
2029:
2028:
2026:
2025:
2020:
2015:
2010:
2005:
2000:
1995:
1990:
1985:
1980:
1975:
1970:
1965:
1960:
1955:
1949:
1947:
1941:
1940:
1938:
1937:
1932:
1931:
1930:
1925:
1915:
1910:
1904:
1902:
1896:
1895:
1893:
1892:
1887:
1882:
1876:
1874:
1873:Summary tables
1870:
1869:
1867:
1866:
1860:
1858:
1852:
1851:
1848:
1847:
1845:
1844:
1843:
1842:
1837:
1832:
1822:
1816:
1814:
1808:
1807:
1805:
1804:
1799:
1794:
1789:
1784:
1779:
1774:
1768:
1766:
1760:
1759:
1757:
1756:
1751:
1746:
1745:
1744:
1739:
1734:
1729:
1724:
1719:
1714:
1709:
1707:Contraharmonic
1704:
1699:
1688:
1686:
1677:
1667:
1666:
1654:
1653:
1651:
1650:
1645:
1639:
1636:
1635:
1628:
1627:
1620:
1613:
1605:
1597:
1596:
1587:
1575:
1559:
1542:
1541:
1539:
1536:
1521:
1517:
1511:
1507:
1486:
1481:
1477:
1471:
1467:
1463:
1460:
1457:
1454:
1451:
1446:
1442:
1438:
1433:
1429:
1425:
1422:
1419:
1408:
1407:
1396:
1393:
1390:
1387:
1382:
1379:
1375:
1371:
1368:
1365:
1362:
1359:
1356:
1353:
1348:
1345:
1341:
1337:
1334:
1331:
1328:
1325:
1320:
1317:
1313:
1309:
1306:
1303:
1300:
1297:
1294:
1289:
1285:
1259:
1255:
1230:
1225:
1221:
1205:
1204:
1193:
1190:
1187:
1184:
1181:
1178:
1175:
1172:
1162:
1158:
1154:
1151:
1146:
1142:
1138:
1133:
1129:
1125:
1122:
1119:
1116:
1111:
1107:
1103:
1098:
1094:
1090:
1087:
1084:
1055:
1051:
1039:
1038:
1024:
1019:
1015:
1005:
1001:
995:
991:
983:
979:
975:
971:
964:
961:
956:
952:
948:
943:
939:
935:
932:
907:
903:
880:
876:
841:random effects
828:
825:
811:
807:
797:
793:
767:
751:
747:
743:
736:
729:
722:
716:
713:is modeled as
709:
702:
697:
696:
685:
682:
679:
674:
671:
667:
663:
658:
655:
651:
647:
642:
638:
634:
631:
626:
621:
618:
615:
611:
605:
600:
597:
594:
590:
584:
581:
578:
574:
557:
550:
543:
536:
530:
515:
505:
502:
489:
484:
481:
477:
473:
470:
467:
462:
459:
455:
451:
448:
443:
439:
418:
413:
410:
406:
402:
399:
396:
391:
388:
384:
380:
377:
372:
368:
345:
342:
338:
315:
312:
308:
296:panel analysis
282:
281:
264:
263:
219:
217:
210:
203:
202:
164:
162:
155:
148:
147:
83:. Please help
69:
67:
60:
55:
29:
28:
26:
19:
9:
6:
4:
3:
2:
3964:
3953:
3950:
3948:
3945:
3943:
3940:
3938:
3935:
3934:
3932:
3917:
3916:
3907:
3905:
3904:
3895:
3893:
3892:
3887:
3881:
3879:
3878:
3869:
3868:
3865:
3851:
3848:
3846:
3845:Geostatistics
3843:
3841:
3838:
3836:
3833:
3831:
3828:
3827:
3825:
3823:
3819:
3813:
3812:Psychometrics
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3783:
3780:
3778:
3775:
3773:
3770:
3768:
3765:
3764:
3762:
3760:
3756:
3750:
3747:
3745:
3742:
3740:
3736:
3733:
3731:
3728:
3726:
3723:
3721:
3718:
3717:
3715:
3713:
3709:
3703:
3700:
3698:
3695:
3693:
3689:
3686:
3684:
3681:
3680:
3678:
3676:
3675:Biostatistics
3672:
3668:
3664:
3659:
3655:
3637:
3636:Log-rank test
3634:
3633:
3631:
3627:
3621:
3618:
3617:
3615:
3613:
3609:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3584:
3582:
3580:
3576:
3573:
3571:
3567:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3533:
3531:
3529:
3525:
3519:
3516:
3514:
3511:
3509:
3507:(BoxâJenkins)
3503:
3501:
3498:
3496:
3493:
3489:
3486:
3485:
3484:
3481:
3480:
3478:
3476:
3472:
3466:
3463:
3461:
3460:DurbinâWatson
3458:
3456:
3450:
3448:
3445:
3443:
3442:DickeyâFuller
3440:
3439:
3437:
3433:
3427:
3424:
3422:
3419:
3417:
3416:Cointegration
3414:
3412:
3409:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3391:Decomposition
3389:
3388:
3386:
3382:
3379:
3377:
3373:
3363:
3360:
3359:
3358:
3355:
3354:
3353:
3350:
3346:
3343:
3342:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3302:
3300:
3298:
3294:
3288:
3285:
3283:
3280:
3278:
3275:
3273:
3270:
3268:
3265:
3263:
3262:Cohen's kappa
3260:
3259:
3257:
3255:
3251:
3247:
3243:
3239:
3235:
3231:
3226:
3222:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3189:
3187:
3185:
3181:
3175:
3171:
3167:
3161:
3159:
3156:
3155:
3153:
3151:
3147:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3115:Nonparametric
3113:
3111:
3108:
3107:
3105:
3101:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3076:
3074:
3072:
3068:
3062:
3059:
3057:
3054:
3052:
3049:
3047:
3044:
3042:
3039:
3038:
3036:
3034:
3030:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3005:
3003:
3001:
2997:
2993:
2986:
2983:
2981:
2978:
2977:
2973:
2969:
2953:
2950:
2949:
2948:
2945:
2943:
2940:
2938:
2935:
2931:
2928:
2926:
2923:
2922:
2921:
2918:
2917:
2915:
2913:
2909:
2899:
2896:
2892:
2886:
2884:
2878:
2876:
2870:
2869:
2868:
2865:
2864:Nonparametric
2862:
2860:
2854:
2850:
2847:
2846:
2845:
2839:
2835:
2834:Sample median
2832:
2831:
2830:
2827:
2826:
2824:
2822:
2818:
2810:
2807:
2805:
2802:
2800:
2797:
2796:
2795:
2792:
2790:
2787:
2785:
2779:
2777:
2774:
2772:
2769:
2767:
2764:
2762:
2759:
2757:
2755:
2751:
2749:
2746:
2745:
2743:
2741:
2737:
2731:
2729:
2725:
2723:
2721:
2716:
2714:
2709:
2705:
2704:
2701:
2698:
2696:
2692:
2682:
2679:
2677:
2674:
2672:
2669:
2668:
2666:
2664:
2660:
2654:
2651:
2647:
2644:
2643:
2642:
2639:
2635:
2632:
2631:
2630:
2627:
2625:
2622:
2621:
2619:
2617:
2613:
2605:
2602:
2600:
2597:
2596:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2572:
2570:
2567:
2566:
2564:
2562:
2558:
2552:
2549:
2545:
2542:
2538:
2535:
2533:
2530:
2529:
2528:
2525:
2524:
2523:
2520:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2497:
2496:
2493:
2492:
2490:
2488:
2484:
2481:
2479:
2475:
2469:
2466:
2464:
2461:
2457:
2454:
2453:
2452:
2449:
2447:
2444:
2440:
2439:loss function
2437:
2436:
2435:
2432:
2428:
2425:
2423:
2420:
2418:
2415:
2414:
2413:
2410:
2408:
2405:
2403:
2400:
2396:
2393:
2391:
2388:
2386:
2380:
2377:
2376:
2375:
2372:
2368:
2365:
2363:
2360:
2358:
2355:
2354:
2353:
2350:
2346:
2343:
2341:
2338:
2337:
2336:
2333:
2329:
2326:
2325:
2324:
2321:
2317:
2314:
2313:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2293:
2291:
2289:
2285:
2281:
2277:
2272:
2268:
2254:
2251:
2249:
2246:
2244:
2241:
2239:
2236:
2235:
2233:
2231:
2227:
2221:
2218:
2216:
2213:
2211:
2208:
2207:
2205:
2201:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2161:
2159:
2157:
2153:
2147:
2144:
2142:
2141:Questionnaire
2139:
2137:
2134:
2130:
2127:
2125:
2122:
2121:
2120:
2117:
2116:
2114:
2112:
2108:
2102:
2099:
2097:
2094:
2092:
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845:fixed effects
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820:joint density
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804:A = E and B=E
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165:This article
163:
154:
153:
144:
141:November 2015
133:
130:
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123:
119:
116:
112:
109:
105:
102: â
101:
97:
96:Find sources:
90:
86:
82:
76:
75:
74:single source
70:This article
68:
64:
59:
58:
53:
51:
44:
43:
38:
37:
32:
27:
18:
17:
3937:M-estimators
3913:
3901:
3882:
3875:
3787:Econometrics
3737: /
3720:Chemometrics
3697:Epidemiology
3690: /
3663:Applications
3505:ARIMA model
3452:Q-statistic
3401:Stationarity
3297:Multivariate
3240: /
3236: /
3234:Multivariate
3232: /
3172: /
3168: /
2942:Bayes factor
2841:Signed rank
2753:
2727:
2719:
2707:
2402:Completeness
2238:Cohort study
2136:Opinion poll
2071:Missing data
2058:Study design
2013:Scatter plot
1935:Scatter plot
1928:Spearman's Ď
1890:Grouped data
1590:
1409:
1242:
1206:
1069:
1040:
861:
856:
830:
815:
803:
791:
786:
780:M-estimators
777:
772:
765:
761:
757:
741:
734:
727:
720:
714:
707:
700:
698:
555:
548:
541:
534:
528:
525:
513:
507:
285:
270:
252:
243:
236:Please help
232:
221:
191:
182:
166:
138:
128:
121:
114:
107:
95:
71:
47:
40:
34:
33:Please help
30:
3915:WikiProject
3830:Cartography
3792:Jurimetrics
3744:Reliability
3475:Time domain
3454:(LjungâBox)
3376:Time-series
3254:Categorical
3238:Time-series
3230:Categorical
3165:(Bernoulli)
3000:Correlation
2980:Correlation
2776:JarqueâBera
2748:Chi-squared
2510:M-estimator
2463:Asymptotics
2407:Sufficiency
2174:Interaction
2086:Replication
2066:Effect size
2023:Violin plot
2003:Radar chart
1983:Forest plot
1973:Correlogram
1923:Kendall's Ď
504:Description
294:method for
240:if you can.
3947:Panel data
3931:Categories
3782:Demography
3500:ARMA model
3305:Regression
2882:(Friedman)
2843:(Wilcoxon)
2781:Normality
2771:Lilliefors
2718:Student's
2594:Resampling
2468:Robustness
2456:divergence
2446:Efficiency
2384:(monotone)
2379:Likelihood
2296:Population
2129:Stratified
2081:Population
1900:Dependence
1856:Count data
1787:Percentile
1764:Dispersion
1697:Arithmetic
1632:Statistics
1538:References
833:panel data
800:) is A BA
754: ; θ)
288:panel data
246:March 2018
185:April 2018
111:newspapers
36:improve it
3163:Logistic
2930:posterior
2856:Rank sum
2604:Jackknife
2599:Bootstrap
2417:Bootstrap
2352:Parameter
2301:Statistic
2096:Statistic
2008:Run chart
1993:Pie chart
1988:Histogram
1978:Fan chart
1953:Bar chart
1835:L-moments
1722:Geometric
1459:
1364:−
1327:
1305:∑
1284:ℓ
1229:⋅
1183:…
1157:μ
1102:∣
1086:
990:μ
978:μ
974:−
947:∣
681:θ
662:∣
633:
610:∑
589:∑
583:Θ
580:∈
577:θ
469:…
398:…
81:talk page
42:talk page
3877:Category
3570:Survival
3447:Johansen
3170:Binomial
3125:Isotonic
2712:(normal)
2357:location
2164:Blocking
2119:Sampling
1998:QâQ plot
1963:Box plot
1945:Graphics
1840:Skewness
1830:Kurtosis
1802:Variance
1732:Heronian
1727:Harmonic
760:= 1,...,
222:require
3903:Commons
3850:Kriging
3735:Process
3692:studies
3551:Wavelet
3384:General
2551:Plug-in
2345:L space
2124:Cluster
1825:Moments
1643:Outline
810:given x
784:√
224:cleanup
171:Please
125:scholar
3772:Census
3362:Normal
3310:Manova
3130:Robust
2880:2-way
2872:1-way
2710:-test
2381:
1958:Biplot
1749:Median
1742:Lehmer
1684:Center
893:given
802:where
706:given
533:given
429:given
328:given
127:
120:
113:
106:
98:
3396:Trend
2925:prior
2867:anova
2756:-test
2730:-test
2722:-test
2629:Power
2574:Pivot
2367:shape
2362:scale
1812:Shape
1792:Range
1737:Heinz
1712:Cubic
1648:Index
290:is a
132:JSTOR
118:books
3629:Test
2829:Sign
2681:Wald
1754:Mode
1692:Mean
862:The
773:E.
104:news
2809:BIC
2804:AIC
1456:exp
1324:log
866:of
843:or
816:B=A
796:- θ
794:MLE
630:log
573:max
540:as
175:to
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