On Bias Reduction in Robust Inference for Generalized Linear Models

It is well known that one or more outlying points in the data may adversely affect the consistency of the quasi-likelihood or the likelihood estimators for the regression effects. Similar to the quasi-likelihood approach, the existing outliers-resistant Mallow's type quasi-likelihood (MQL) estimation approach may also produce biased regression estimators. As a remedy, by using a fully standardized score function in the MQL estimating equation, in this paper, we demonstrate that the fully standardized MQL estimators are almost unbiased ensuring its higher consistency performance. Both count and binary responses subject to one or more outliers are used in the study. The small sample as well as asymptotic results for the competitive estimators are discussed. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.