多维广义线性模型拟极大似然估计的弱相合性  

Weak Consistency of Quasi-Maximum Likelihood Estimates in Multivariate Generalized Linear Models

作　　者：廖源[1] 张三国[1] 薛宏旗[1] 

机构地区：[1]中国科学院研究生院数学系,北京100049

出　　处：《应用概率统计》2006年第3期288-294,共7页Chinese Journal of Applied Probability and Statistics

基　　金：partly supported by National Natural Science Foundation of China and President Foundation of GUCAS.

摘　　要：本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to n X_iX_i^1的最小特征值．In this paper, we study quasi-likelihood equation ^n∑i=1Xi（yi-μ（Xi^1β））=0 for multivariate generalized linear lnodels （GLMs）. Under mild conditions, we prove the asymptotic existence of the solution βn to the above equation and present its convergence rate, that is βn-βo = Op（λ2n-1/2）, where βo is the true value of parameter β and λn denotes the smallest smallest eigenvalue of the matrix Sn=^n∑i=1XiXi^1

关 键 词：多维广义线性模型 拟极大似然估计 弱相合性 收敛速度 

分 类 号：O212.1[理学—概率论与数理统计]