Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative
Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative
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DOI：
10.1093/biomet/92.3.507
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发表时间：
2005-09-01
期刊：
影响因子：
2.7
通讯作者：
Skovgaard, IM
中科院分区：
文献类型：
--
作者：
Ritz, C;Skovgaard, IM
对于指数族的子模型，我们考虑使某些参数不可识别的假设的似然比检验。首先，我们建立了似然比检验与得分检验的渐近等价性。其次，利用得分检验表示法推导出似然比检验的渐近分布。这些结果是在不假定参数空间紧性的情况下，对指数族的通用子模型得到的。然后，我们举例说明了一类多元正态模型的结果，其中关于协方差结构的零假设会导致参数的可辨识性的损失。我们在整篇文章中的动机问题是测试一个随机截获模型与一个允许序列相关的可选协方差结构。
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.