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We consider the problem of robust inference under the generalized linearmodel (GLM) with stochastic covariates. We derive the properties of the minimumdensity power divergence estimator of the parameters in GLM with random designand use this estimator to propose robust Wald-type tests for testing anygeneral composite null hypothesis about the GLM. The asymptotic and robustnessproperties of the proposed tests are also examined for the GLM with randomdesign. Application of the proposed robust inference procedures to the popularPoisson regression model for analyzing count data is discussed in detail boththeoretically and numerically through simulation studies and real dataexamples.

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