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

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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces a new family of estimators, MDPDE, as a robust generalization of MLE for loglinear models using the DPD measure. Confidence intervals and robust Wald-type test statistics are developed based on these estimators. The robust properties of MDPDE and Wald-type tests are theoretically studied through influence function analysis, with simulation study confirming the validity of the results.