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

Abstract

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 Lai , T. L. , Robbins , H. , Wei , C. Z. ( 1979 ). Strong consistency of least squares estimates in multiple regression II . J. Multivariate Anal. 9 : 343 – 361 .[Crossref], [Web of Science ®] , [Google Scholar]), 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.