广义线性模型极大似然估计的强相合性与渐近正态性
Strong Consistency and Asymptotic Normality of Maximum Likelihood Estimates in Generalized Linear Models
-
摘要: 本文研究了若干重要类型的离散响应变量广义线性模型,在\sum\limits_i=1^n\mathop\Zeta _i\mathop\Zeta _i^l的最小特征根大于cnα(对某个c>0,α>0)等条件下证明了回归参数向量的极大似然估计的强相合性与渐近正态性,其中设计阵序列||Z_n||可以为无界序列.Abstract: 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≥cnα 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.