Asymptotic Properties of the Maximum Quasi-Likelihood Estimator in Quasi-Likelihood Nonlinear Models

Abstract

Quasi-likelihood nonlinear models (QLNM) are a further extension of generalized linear models by only specifying the expectation and variance functions of the response variable. In this article, some mild regularity conditions are proposed. These regularity conditions, respectively, assure the existence, strong consistency, and the asymptotic normality of the maximum quasi-likelihood estimator (MQLE) in QLNM.

Keywords:

• Asymptotic normality
• Consistency
• Maximum quasi-likelihood estimator
• Quasi-likelihood nonlinear models

Mathematics Subject Classification:

• Primary 62F12, 62G02
• Secondary 62G12

Acknowledgments

The authors wish to thank the referee and editor for valuable comments which have greatly improved the article. This work was partially supported by Natural Science Foundation of China (10761011), Mathematical Tianyuan Fund of National Science Foundation of China (10626048), Natural Science Foundations of Yunnan University (2005Z007C), and Special Foundation for Middle and Young Excellent Teachers of Yunnan University.