协方差结构分析中拟似然估计的对偶几何方法  

ANALYSIS OF COVARIANCE STRUCTURESBY QUASI-LIKELIHOOD WITH DUAL GEOMETRICAL APPROACH

作　　者：韦博成[1] 王树佳[2] 

机构地区：[1]东南大学数学系,南京210096 [2]深圳大学软件学系,广东深圳518000

出　　处：《数学年刊（A辑）》2002年第4期439-446,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19631040)资助的项目.

摘　　要：本文应用几何方法研究了协方差结构分析中的拟似然估计.对于该模型引进了对偶几何,在此基础上得到了拟似然估计的二阶渐近性质.通过对偶曲率给出了拟似然估计的偏差、方差和信息损失,并且给出了反映拟观察信息和拟期望信息之间关系的一个极限定理.The quasi-likelihood estimation in analysis of covariance structure is investigated via a geometric approach. A dual geometry is introduced into the model. Some second-order asymptotic results of the quasi-likelihood estimate based on the dual geometry are obtained. The bias, covariance matrix and information loss of quasi-likelihood estimate are interpreted by the dual curvature. A limit theorem that reflects the relationship between the quasi-observed and the quasi-expected information is also established.

关 键 词：协方差结构分析 曲率 对偶几何 Fisher信息 信息损失 拟似然 

分 类 号：O212.4[理学—概率论与数理统计]