Model checking in loglinear models using phi-divergences and MLEs



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Cressie, Noel A. and Pardo Llorente, Leandro (2002) Model checking in loglinear models using phi-divergences and MLEs. Journal of statistical planning and inference, 103 (1-2). pp. 437-453. ISSN 0378-3758

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Consider the loglinear model for categorical data under the assumption of either Poisson, multinomial, or product-multinomial sampling. We are interested in testing between various hypotheses on the parameter space. In this paper, the usual likelihood ratio test, with maximum likelihood estimators for the unspecified parameters, is generalized to tests based on phi-divergences, still using maximum likelihood estimators. These tests yield the likelihood ratio test as a special case. Asymptotic distributions for the new test statistics are derived under both the null and the alternative hypotheses. Then it is shown how the phi-divergences can be used to test nested hypotheses, yielding a type of "analysis of divergence".

Item Type:Article
Uncontrolled Keywords:asymptotic distributions; nested hypotheses; Poisson sampling; multinomial sampling; product-multinomial sampling;of-fit tests; discrete-distributions.
Subjects:Sciences > Mathematics > Applied statistics
ID Code:17840
Deposited On:22 Jan 2013 12:19
Last Modified:25 Jun 2018 11:46

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