Robustness of Minimum Density Power Divergence Estimators and Wald-type test statistics in loglinear models with multinomial sampling

Abstract

In this paper we propose a new family of estimators, Minimum Density Power Divergence Estimators (MDPDE), as a robust generalization of maximum likelihood estimators (MLE) for the loglinear model with multinomial sampling by using the Density Power Divergence (DPD) measure introduced by Basu et al. (1998). Based on these estimators, we further develop two types of confidence intervals (asymptotic and bootstrap ones), as well as a new robust family of Wald-type test statistics for testing a nested sequence of loglinear models. Furthermore, we study theoretically the robust properties of both the MDPDE as well as Wald-type tests through the classical influence function analysis. Finally, a simulation study provides further confirmation of the validity of the theoretical results established in the paper.