Abstract
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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Ding, J.L., Chen, X.R. Asymptotic Properties of the Maximum Likelihood Estimate in Generalized Linear Models with Stochastic Regressors. Acta Math Sinica 22, 1679–1686 (2006). https://doi.org/10.1007/s10114-005-0693-3
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DOI: https://doi.org/10.1007/s10114-005-0693-3