Rate of Strong Consistency of Maximum Quasi-Likelihood Estimator in Multivariate Generalized Linear Models

Abstract

In this article, we consider a multivariate generalized linear model with adaptive design matrix and general link function. The asymptotic singularity of design matrix of adaptive design presents challenge when establishing the large sample properties of the maximum quasi-likelihood estimate (MQLE). Under some mild conditions, we obtain a strong convergence rate of the MQLE.

Keywords:

• Maximum quasi-likelihood estimator
• Multivariate generalized linear models
• Strong consistency rate

Mathematics Subject Classification:

• Primary 62F12
• Secondary 62J12

Acknowledgments

We are grateful to the Associate Editor and two reviewers for their insightful comments. This work was partially supported by the National Natural Science Foundation of China (10671189, 10701067), the Knowledge Innovation Program of the Chinese Academy of Science, and the Natural Science Foundation of Guangxi and Guangxi University.