Asymptotic Normality of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed Design

Received: 22 August 2007 / Revised: 7 April 2008 c ©2008 Springer Science + Business Media, LLC Abstract In generalized linear models with fixed design, under the assumption λn → ∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator β̂n, which is the root of the quasi-likelihood equation with natural link function ∑n i=1 Xi(yi−μ(X ′ iβ)) = 0, is obtained, where λn denotes the minimum eigenvalue of ∑n i=1 XiX ′ i, Xi are bounded p× q regressors, and yi are q × 1 responses.