Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative
成果类型：
Article
署名作者：
Ritz, C; Skovgaard, IM
署名单位：
University of Copenhagen
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/92.3.507
发表日期：
2005
页码：
507517
关键词：
摘要：
For submodels of an exponential family, we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable. First, we establish the asymptotic equivalence between the likelihood ratio test and the score test. Secondly, the score-test representation is used to derive the asymptotic distribution of the likelihood ratio test. These results are derived for general submodels of an exponential family without assuming compactness of the parameter space. We then exemplify the results on a class of multivariate normal models, where null hypotheses concerning the covariance structure lead to loss of identifiability of a parameter. Our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation.
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