Minimum <Emphasis Type="Italic">Φ</Emphasis>-Divergence Estimator and <Emphasis Type="Italic">Φ</Emphasis>-Divergence Statistics in Generalized Linear Models with Binary Data

In this paper, we assume that the data are distributed according to a binomial distribution whose probabilities follow a generalized linear model. To fit the data the minimum φ-divergence estimator is studied as a generalization of the maximum likelihood estimator. We use the minimum φ-divergence estimator, which is the basis of some new statistics, for solving the problems of testing in a generalized linear model with binary data. A wide simulation study is carried out for studying the behavior of the new family of estimators as well as of the new family of test statistics. This work was partially supported by Grant MTM2006-06872 and UCM2006-910707.