LIKELIHOOD DIVERGENCE STATISTICS FOR TESTING HYPOTHESES ABOUT MULTIPLE POPULATION

Abstract

The problem of introducing divergence-based statistics to test composite hypotheses related to s populations is still open when sample sizes are not equal. On the basis of likelihood divergence statistics, a statistical procedure is introduced in this paper and its large sample behaviour is studied. By using Rényi divergence, the proposed statistical procedure is applied to the problem of testing for the homogeneity of several variances. Members of the family of likelihood Rényi divergence statistics are compared for power and checked for fidelity to type I error rates with some classical test statistics. Results of the Monte Carlo simulation study are discussed and presented in tables.

Keywords:

• Rényi divergence
• Likelihood divergence statistics
• Testing hypotheses
• Homogeneity of variances
• Multiple population

ACKNOWLEDGMENTS

The research in this paper was supported in part by the grants BMF2000-0800 and GV99-159-1-01. Their financial support is gratefully acknowledged.