A robust approach for generalized linear models based on maximum Lq-likelihood procedure

TL;DR

This paper introduces a robust estimation method for generalized linear models using maximum Lq-likelihood, extending traditional algorithms and providing tools for model selection and outlier detection.

Contribution

It presents a novel robust estimation procedure based on maximum Lq-likelihood for generalized linear models, including an extended algorithm and new diagnostic tools.

Findings

The method performs well in simulations under contaminated data.

Robust deviance and AIC improve model selection accuracy.

Application to real data demonstrates practical utility.

Abstract

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.