In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual iteratively weighted least squares method in generalized linear models is presented. It is through the discussion of the asymptotic distribution of the proposed estimator and a set of statistics for testing linear hypothesis that it is possible to define standardized residuals using the mean-shift outlier model. In addition, robust versions of deviance function and the Akaike information criterion are defined with the aim of providing tools for model selection. Finally, the performance of the proposed methodology is illustrated through a simulation study and analysis of a real dataset.

翻译：本文提出了一种基于最大Lq似然法的广义线性模型稳健估计方法。同时，我们提出了一种估计算法，该算法是广义线性模型中常规迭代加权最小二乘法的自然扩展。通过讨论所提估计量的渐近分布以及用于检验线性假设的统计量集合，我们可以利用均值平移离群值模型定义标准化残差。此外，本文定义了偏差函数和赤池信息准则的稳健版本，旨在为模型选择提供工具。最后，通过模拟研究和真实数据集分析，展示了所提方法的性能。