Empirical phi-divergence test statistics in the logistic regression model

TL;DR

This paper introduces a new family of empirical phi-divergence test statistics for logistic regression, extending the empirical likelihood ratio test and analyzing their asymptotic behavior and power through simulations.

Contribution

It defines and studies a novel family of divergence-based test statistics for logistic regression, demonstrating their asymptotic equivalence and consistency.

Findings

Asymptotic distribution matches classical empirical likelihood ratio test.

Empirical phi-divergence tests are consistent in the Fraser sense.

Simulation study compares behavior of new test statistics.

Abstract

In this paper we apply divergence measures to empirical likelihood applied to logistic regression models. We define a family of empirical test statistics based on divergence measures, called empirical phi-divergence test statistics, extending the empirical likelihood ratio test. We study the asymptotic distribution of these empirical test statistics, showing that it is the same for all the test statistics in this family, and the same as the classical empirical likelihood ratio test. Next, we study the power function for the members in this family, showing that the empirical phi-divergence tests introduced in the paper are consistent in the Fraser sense. In order to compare the differences in behavior among the empirical phi-divergence test statistics in this new family, considered for the first time in this paper, we carry out a simulation study.