Analysis of Robust Quasi-deviances for Generalized Linear Models

Generalized linear models (McCullagh and Nelder'89) are a popular technique for modeling a large variety of continuous and discrete data. They assume that the response variables Yi , for i = 1, . . . , n, come from a distribution belonging to the exponential family, such that E[Yi ] = µi and V[Yi ] = V (µi ), and that ηi = g(µi ) = xiTβ, where β ∈ IR p is the vector of parameters, xi ∈ IR p, and g(.) is the link function.The non-robustness of the maximum likelihood and the maximum quasi-likelihood estimators has been studied extensively in the literature. For model selection, the classical analysis-of-deviance approach shares the same bad robustness properties. To cope with this, Cantoni and Ronchetti (2001) propose a robust approach based on robust quasi-deviance functions for estimation and variable selection. We refer to that paper for a deeper discussion and the review of the literature.