Using power-divergence statistics to test for homogeneity in product-multinomial distributions

Authors

Noel Cressie, University of WollongongFollow
Frederck M. Medak, Iowa State University

RIS ID

71990

Publication Details

Cressie, N. & Medak, F. M. (2011). Using power-divergence statistics to test for homogeneity in product-multinomial distributions. In L. Pardo, N. Balakrishnan & M. Gil (Eds.), Modern Mathematical Tools and Techniques in Capturing Complexity (pp. 157-175). United States: Springer.

Abstract

Testing for homogeneity in the product-multinomial distribution, where the hypotheses are hierarchical, uses maximum likelihood estimation and the loglikelihood ratio statistic G ². We extend these ideas to the power-divergence family of test statistics, which is a one-parameter family of goodness-of-fit statistics that includes the loglikelihood ratio statistic G ², Pearson's X ², the Freeman-Tukey statistic, the modified loglikelihood ratio statistic, and the Neyman-modified chi-squared statistic. Explicit minimum-divergence estimators can be obtained for all members of the one-parameter family, which allows a straightforward analysis of divergence. An analysis of fourteen retrospective studies on the association between smoking and lung cancer demonstrates the ease of interpretation of the resulting analysis of divergence.