1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2. Graduate School, Chinese Academy of Science, Beijing 100049, China
Abstract:
This paper gives a thorough theoretical treatment on the adaptive quasi-likelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.