王健發(fā)，肖澤青，王瀘怡

（廣西大學(xué) 數(shù)學(xué)與信息科學(xué)學(xué)院，廣西 南寧 530004）

廣義線性模型中擬似然估計的弱相合性及漸近正態(tài)性

王健發(fā)，肖澤青，王瀘怡

（廣西大學(xué) 數(shù)學(xué)與信息科學(xué)學(xué)院，廣西 南寧 530004）

擬似然估計；弱相合性；漸近正態(tài)性

廣義線性模型（GLMS）由Nelder和Wedderburn[1]引入，作為一種處理非正態(tài)響應(yīng)變量的回歸分析模型，其定義如下

其中yi是q維響應(yīng)變量,Xi是p×q設(shè)計矩陣.h∶Rq→Rq是充分光滑的一一映射，β∈Rp是未知的回歸參數(shù)，β0是它的真值，函數(shù)h的逆稱為聯(lián)系函數(shù).給定Xi的條件下，yi( )i=1,…,n獨立且有如下的指數(shù)分布：

其中：θi稱為自然參數(shù)；b()·,c()·為相應(yīng)于指數(shù)分布的確定函數(shù).對數(shù)似然方程由b(·)和h(·)可求得 ∑(·).在許多情形下假定yi服從指數(shù)分布（2）是不切實際的，而且∑(·)的確切表達式不知道.但如果期望（1）假定是正確的，我們?nèi)钥捎肳edderburm引入的擬似然方法，用擬似然方程

1 主要結(jié)果

2 定理的證明

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[7]高啟兵,吳耀華.廣義線性回歸擬似然估計的強相合性[J].數(shù)學(xué)年刊:A輯,2004,25(6):705-710.

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Weak Consistency and Asymptotic Normality of Quasi-Maximum Likelihood Estimates in Generalized Linear Models

WANG Jianfa，XIAO Zeqing，WANG Luyi
（School of Mathematics and Information Science，Guangxi University，Nanning530004，China）

In a generalized linear model withq×1 responses,bounded and fixedp×qregressorsXiand natural link func?tion,we study the solutionof quasi-maximum likelihood equationand other conditions,and use contractive mappings to prove that the quasi-likelihood equation has a solutionof weak consistency;Fort＞0,let ψ(t) be a positive nondecreasing function such thatis a convex function,which prove the asymptotic normality of maximum quasi-likehood estimatorβn.

quasi-maximum likelihood estimation；weak consistency；asymptotic normality

O 212.1

A

1674-4942（2011）02-0137-04

2011-01-25

國家自然科學(xué)基金（11061002）

畢和平