On tests of independence based on minimum phi-divergence estimator with constraints: An application to modeling DNA

Abstract

A new family of estimators, Minimum phi-divergence estimators, is introduced for the problem of independence in a two-way contingency table and their asymptotic properties are studied. Based on this new family of estimators, a new family of test statistics for the problem of independence is defined. This new family of test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. A simulation study is presented to show that some new test statistics offer an attractive alternative to the classical Pearson and likelihood ratio test statistics for this problem. The procedures proposed in this paper can be used for testing positional independence of a DNA sequence as it is illustrated by a numerical example.