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Size and power considerations for testing loglinear models using phi-divergence test statistics

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Cressie, Noel A. and Pardo Llorente, Leandro and Pardo Llorente, María del Carmen (2003) Size and power considerations for testing loglinear models using phi-divergence test statistics. Statistica Sinica, 13 (2). pp. 555-570. ISSN 1017-0405

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Official URL: http://www3.stat.sinica.edu.tw/statistica/oldpdf/A13n218.pdf




Abstract

In this article, we assume that categorical data axe distributed according to a multinomial distribution whose probabilities follow a loglinear model. The inference problem we consider is that of hypothesis testing in a loglinear-model setting. The null hypothesis is a composite hypothesis nested within the alternative. Test statistics are chosen from the general class of phi-divergence statistics. This article collects together the operating characteristics of the hypothesis test based on both asymptotic (using large-sample theory) and finite-sample (using a designed simulation study) results. Members of the class of power divergence statistics are compared, and it is found that the Cressie-Read statistic offers an attractive alternative to the Pearson-based and the likelihood ratio-based test statistics, in terms of both exact and asymptotic size and power.


Item Type:Article
Uncontrolled Keywords:Chi-squared distribution; contiguous alternatives; multinomial distribution; nested hypotheses; noncentral chi-squared distribution; powerdivergence statistic.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17833
Deposited On:21 Jan 2013 15:17
Last Modified:26 Feb 2015 09:14

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