Asymptotic Properties of Quasi-Maximum Likelihood Estimates in Generalized Linear Models.

In this article, we consider the quasi-likelihood equation for generalized linear models (GLMs). Under some mild conditions, including the convergent system which is defined by Lai et al. (1979), we obtain the asymptotic existence of the solution to the above equation and show that , where β0 is the true value of parameter β and denotes the smallest (largest) eigenvalue of satisfying for given δ > 1. We also present the asymptotic normality of for univariate GLMs, based on which “studentized” large sample confidence intervals for β0 are constructed. Simulation results and related remarks are given. [ABSTRACT FROM AUTHOR]