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

Abstract

In generalized linear models with fixed design, under the assumption$\underline \lambda _n \to \infty$ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator $\hat \beta _n$, which is the root of the quasi-likelihood equation with natural link function $\sum\nolimits_{i = 1}^n {X_i \left( {y_i - \mu \left( {X_i^\prime \beta } \right)} \right) = 0}$, is obtained, where $\underline \lambda _n$ denotes the minimum eigenvalue of $\sum\nolimits_{i = 1}^n {X_i X_i^\prime }$, X _i are bounded p × q regressors, and y _i are q × 1 responses.