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

Chapter


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. © 2011 Springer-Verlag Berlin Heidelberg.

Publication Date


  • 2011

Citation


  • Cressie, N. A. & 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. 157-169). United States: Springer.

Scopus Eid


  • 2-s2.0-80051691332

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2269

Book Title


  • Modern Mathematical Tools and Techniques in Capturing Complexity

Start Page


  • 157

End Page


  • 169

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. © 2011 Springer-Verlag Berlin Heidelberg.

Publication Date


  • 2011

Citation


  • Cressie, N. A. & 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. 157-169). United States: Springer.

Scopus Eid


  • 2-s2.0-80051691332

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2269

Book Title


  • Modern Mathematical Tools and Techniques in Capturing Complexity

Start Page


  • 157

End Page


  • 169