New families of estimators and test statistics in log-linear models

Abstract

In this paper we consider categorical data that are distributed according to a multinomial, product-multinomial or Poisson distribution whose expected values follow a log-linear model and we study the inference problem of hypothesis testing in a log-linear model setting. The family of test statistics considered is based on the family of phi-divergence measures. The unknown parameters in the log-linear model under consideration are also estimated using phi-divergence measures: Minimum phi-divergence estimators. A simulation study is included to find test statistics that offer an attractive alternative to the Pearson chi-square and likelihood-ratio test statistics.