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