Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).