Robust properties of likelihood ratio tests

Kent, John T.

doi:10.1093/biomet/69.1.19

Cited by 144 publications

(127 citation statements)

References 9 publications

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“…However, it seems reasonable to expect that if the restriction holds, then the difference Q n ðũ n ; Y n Þ À Q n ðû n ; Y n Þ will be small. The following result, which can be regarded as generalizing that of Kent [33] on the distribution of likelihood ratios in mis-specified models, makes this precise:…”

Section: Model Comparisonmentioning

confidence: 94%

Estimating functions and the generalized method of moments

Jesus

Chandler

2011

Interface Focus.

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Estimating functions provide a very general framework for statistical inference, and are particularly useful when one is either unable or unwilling to specify a likelihood function. This paper aims to provide an accessible review of estimating function theory that has potential for application to the analysis and modelling of a wide range of complex systems. Assumptions are given in terms that can be checked relatively easily in practice, and some of the more technical derivations are relegated to an online supplement for clarity of exposition. The special case of the generalized method of moments is considered in some detail. The main points are illustrated by considering the problem of inference for a class of stochastic rainfall models based on point processes, with simulations used to demonstrate the performance of the methods.

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Section: Model Comparisonmentioning

confidence: 94%

Estimating functions and the generalized method of moments

Jesus

Chandler

2011

Interface Focus.

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“…By contrast, Wald tests and confidence ellipsoids based on the unadjusted likelihood have asymptotic size equal to one and asymptotic coverage probabilities equal to zero. A further consequence of the failure of the second Bartlett identity is that the adjusted likelihood ratio statistic (i.e., the LR statistic applied to the adjusted likelihood) is, under the null, asymptotically distributed as a weighted sum of χ 2 1 variates with the eigenvalues of − H a (θ 0 ) −1 as weights (instead of being χ 2 p+q asymptotically); see, e.g., Kent (1982), White (1982), and Vuong (1989). Although these weights can be estimated, the adjusted likelihood ratio statistic is unsuited for testing because it is ill-signed for large enough values of ρ.…”

Section: Estimation and Inferencementioning

confidence: 99%

Likelihood Inference in an Autoregression With Fixed Effects

Dhaene

Jochmans

2015

Econom. Theory

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We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

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“…It is well-known that minus twice the LR statistic has a limiting central chi-square distribution under the null hypothesis (Wilks (193 8) ), and a limiting non-central chisquare distribution under a sequence of local alternatives (Wald (1943)) with a non-centrality parameter equal to that of the Wald statistic (Wald (1943)) and Lagrange Multiplier statistic (Aitchinson and Sil vey (1958) , Silvey (1959) ). However , as Foutz and Srivastana 4 (1977) , Kent (1982) , and White (1982a) pointed out, when the largest model is misspecified, the LR statistic is no longer ne cessarily chi square distributed under the null hypothesis where the null hypothesis must be appropriately redefined in terms of the pseudo-true values satisfying the specified restrictions .…”

Section: Introduction Quang H Vuong California Institute Of Technologymentioning

confidence: 99%