The Asymptotic Properties Of Generalized Linear Models

Generalized linear models are important extensions of the linear models, statisticians suggest using generalized linear models to modeling and analysis discrete data. Generalized linear models provide an effective statistical method for statistics. Generalized linear models such as the logistic model, probit model and packet cox model, Gamma distribution model has important applications in biology, agriculture, medicine, astronomy, and other fields. Generalized estimating equation is a method of using generalized linear models to analysis longitudinal data, since its inception, the generalized estimating equation has been great development in theoretical research and application. The main work of this paper includes:firstly, this paper proves the asymptotic normality and strong consistency of regression parameters of the maximum likelihood estimate of the linear Gamma distribution model under mild conditions. Secondly, this paper proved strong consistency of the root of the generalized estimating equations under mild conditions in the following case:observing the number of individuals nâ†'∞, observation times for each individual mâ†'∞, this is an improvement of the corresponding results in the literature.