TY - JOUR
AU - Cantoni, Eva
PY - 2004/04/26
Y2 - 2023/03/23
TI - Analysis of Robust Quasi-deviances for Generalized Linear Models
JF - Journal of Statistical Software
JA - J. Stat. Soft.
VL - 10
IS - 4
SE - Articles
DO - 10.18637/jss.v010.i04
UR - https://www.jstatsoft.org/index.php/jss/article/view/v010i04
SP - 1 - 9
AB - Generalized linear models (McCullagh and Nelder 1989) are a popular technique for modeling a large variety of continuous and discrete data. They assume that the response variables Y<sub>i</sub> , for i = 1, . . . , n, come from a distribution belonging to the exponential family, such that E[Y<sub>i</sub> ] = µ<sub>i</sub> and V[Y<sub>i</sub> ] = V (µ<sub>i</sub> ), and that η<sub>i</sub> = g(µ<sub>i</sub> ) = x<sub>i</sub><sup>T</sup>β, where β ∈ IR <sup>p</sup> is the vector of parameters, x<sub>i</sub> ∈ IR <sup>p</sup>, and g(.) is the link function.</p><p>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.
ER -