Asymptotic Properties of the Maximum Likelihood Estimate in Generalized Linear Models with Stochastic Regressors

Ding, Jie Li; Chen, Xi Ru
October 2006
Acta Mathematica Sinica;Oct2006, Vol. 22 Issue 6, p1679
Academic Journal
For generalized linear models (GLM), in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate (MLE) $$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } _{n} $$ of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of $$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } _{n} $$ .


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