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.

我们考虑具有随机协变量的广义线性模型（GLM）下的鲁棒推理问题。我们采用随机设计推导了GLM中参数的最小密度功率散度估计量的属性，并使用该估计量提出鲁棒的Wald型检验，以测试有关GLM的任何一般复合零假设。对于随机设计的GLM，还检查了所提出测试的渐近性和鲁棒性。通过仿真研究和实际数据示例，从理论和数值上详细讨论了所提出的鲁棒推断程序在流行的Poisson回归模型中用于计数数据分析的应用。