Analysis of ϕ-divergence for loglinear models with constraints under product-multinomial sampling

Abstract

The loglinear model under product-multinomial sampling with constraints is considered. The asymptotic expansion and normality of the restricted minimum ϕ-divergence estimator (RMϕDE) which is a generalization of the maximum likelihood estimator is presented. Then various statistics based on ϕ-divergence and RMϕDE are used to test various hypothesis test problems under the model considered. These statistics contain the classical loglikelihood ratio test statistics and Pearson chi-squared test statistics. In the last section, a simulation study is implemented.