Phi-Divergence Statistics for Testing Linear Hypotheses in Logistic Regression Models

Abstract

In this paper we introduce and study two new families of statistics for the problem of testing linear combinations of the parameters in logistic regression models. These families are based on the phi-divergence measures. One of them includes the classical likelihood ratio statistic and the other the classical Pearson's statistic for this problem. It is interesting to note that the vector of unknown parameters, in the two new families of phi-divergence statistics considered in this paper, is estimated using the minimum phi-divergence estimator instead of the maximum likelihood estimator. Minimum phi-divergence estimators are a natural extension of the maximum likelihood estimator.

Keywords:

• General linear hypotheses
• Logistic regression model
• Minimum phi-divergence estimator
• Phi-divergence statistic

Mathematics Subject Classification:

• Primary 62H15
• Secondary 62H17

Acknowledgments

This work was supported by Grant MTM2006-06872 and UCM2006-910707. The authors would like to thanks a referee for critically reading this paper and making suggestions.