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

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