广义线性模型中极大拟似然估计的强收敛速度

数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 1058-1064.

广义线性模型中极大拟似然估计的强收敛速度

尹长明, 李永明, 王朋炎

(广西大学数学与信息科学学院, 广西南宁 530004)

收稿日期:2007-06-10 修回日期:2008-09-19 出版日期:2009-08-25 发布日期:2009-08-25
基金资助:
广西大学科研基金(DD051005)和广西自然科学基金(0832108, 0575051)资助

Strong Convergence Rates of the Maximum Quasi-Likelihood Estimator in Generalized Linear Models

YIN Chang-Ming, LI Yong-Ming, WANG Peng-Yan

(School of Mathematics and Information |Science, Guangxi University, Guangxi Nanning 530004)

Received:2007-06-10 Revised:2008-09-19 Online:2009-08-25 Published:2009-08-25
Supported by:
广西大学科研基金(DD051005)和广西自然科学基金(0832108, 0575051)资助

摘要/Abstract

摘要：

在sup_{i ≥1}E||y_i||^2+α< ∞(对某个α > 0)和其它正则条件下, 证明了一般联系函数的多维广义线性模型拟似然估计的强相合性, 并得到了强收敛速度, 其中 y_i是响应变量. 此结果是对文献中相应结果的改进.

关键词: 广义线性模型, 拟似然估计, 强相合性, 强收敛速度

Abstract:

In a generalized linear model with q×1 responses, bounded and fixed p×q regressors Z_i and general link function, under the moment
condition on responses as weak as possible and other conditions, the authors prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore. This result is an improvement over the relevant results in literature.

Key words: Generalized linear model, Maximum quasi-likelihood estimate, Strong consistency, , Strong convergence rate

中图分类号:

62F12

尹长明, 李永明, 王朋炎. 广义线性模型中极大拟似然估计的强收敛速度[J]. 数学物理学报, 2009, 29(4): 1058-1064.

YIN Chang-Ming, LI Yong-Ming, WANG Peng-Yan. Strong Convergence Rates of the Maximum Quasi-Likelihood Estimator in Generalized Linear Models[J]. Acta mathematica scientia,Series A, 2009, 29(4): 1058-1064.

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