Title: Robust Wald-type test in GLM with random design based on minimum density power divergence estimators,
Abstract: We consider the problem of robust inference under the important 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 used this estimator to propose a robust Wald-type test for testing
any general composite null hypothesis about the GLM. The asymptotic and
robustness properties of the proposed test 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 with some interesting real data
examples.