Strong Consistency and Asymptotic Normality of Maximum Likelihood Estimates in Generalized Linear Models

For some important generalized linear models with discrete responses, we establish the strong consistency and asymptotic normality of the maximum likelihood estimates of the regression parameter vector, under some mild conditions such as ||Z_n|| =o(logn), \underline\lambda _n≥cn^α for some c＞0, α＞0, where Z_n are regressor and \underline\lambda _n are the minimum eigenvalue of \sum\limits_i=1^n\mathop\Zeta _i\mathop\Zeta _i^l.