多维广义线性模型拟极大似然估计的弱相合性

本文考虑多维广义线性模型的拟似然方程$\tsm^n_{i=1}X_i(y_i-\mu(X_i'\xb))=0$, 在一定条件下证明了此方程的解$\wh\xb_n$渐近存在, 并得到了其收敛速度, 即$\wh\xb_n-\xb_0=O_p({\underline{\xl}}_n^{-1/2})$, 其中$\xb_0$为参数$\xb$的真值, $\underline{\xl}_n$是方阵$S_n=\tsm^n_{i=1}X_iX_i'$的最小特征值。

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

In this paper, we study quasi-likelihood equation n∑i=1 Xi(yi -μ(X'iβ)) = 0 for multivariategeneralized linear models (GLMs). Under mild conditions, we prove the asymptotic existence of the solution (β)n to the above equation and present its convergence rate, that is (β)n - β0 =Op((λ)n-1/2), where β0 is the true value of parameter β and (λ)n denotes the smallest eigenvalue of the matrix Sn = n∑i=1 XiX'i.