%0 Journal Article
%T Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear Models<br>广义线性回归极大似然估计的强相合性
%A Ding Jieli
%A Chen Xiru
%A <br>丁洁丽
%A 陈希孺
%J 数学物理学报(A辑)
%D 2006
%I 
%X Assuming the generalized linear model as described in \S1, let $\underline{\lambda}_n$and $\overline{\lambda}_n$ denote the minimum and maximum eigentvalues of$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$ resp., and$\hat{\beta}_n$ denote the maximum likelihood estimator of $\beta_0$. It is shown in 1] that, when \{$Z_i,i\ge1$\}is bounded, the sufficient conditions for strong consistency of $\hat{\beta}_n$ are as follows:$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$(for some $\delta>0$) with natural link function, and $\underline{\lambda}_n\rightarrow\infty$,$\overline{\lambda}_n=O(\underline{\lambda}_n)$ with nonnatural link function resp.. In this paper, the authors improvethe latter result by showing that even in the case of nonnatural link function, the condition$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$ remains to be sufficient.
%K Generalized linear model
%K Maximum likelihood estimate
%K Strong consistency<br>广义线性模型
%K 极大似然估计
%K 强相合性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=1DA8121F29331EDA&yid=37904DC365DD7266&vid=96C778EE049EE47D&iid=0B39A22176CE99FB&sid=BBF7D98F9BEDEC74&eid=DABEF202280E7EF1&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=7