Robust Wald-type test in GLM with random design based on minimum density power divergence estimators

TL;DR

This paper develops robust Wald-type tests for generalized linear models with random covariates using minimum density power divergence estimators, enhancing inference robustness against data contamination.

Contribution

It introduces a new robust inference method for GLMs with stochastic covariates based on minimum density power divergence estimators, with theoretical and practical validation.

Findings

Proposed tests are asymptotically robust and reliable.

Application to Poisson regression demonstrates effectiveness.

Simulation and real data confirm robustness and accuracy.

Abstract

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.