广义线性模型拟似然估计的弱相合性

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

研究了广义线性模型在非典则联结情形下的拟似然方程Ln(β)=∑ni=1XiH(X'iβ)Λ-1(X'iβ)(yi-h(X'iβ))=0的解βn在一定条件下的弱相合性,证明了收敛速度βn-β0≠op(λn-1/2)以及拟似然估计的弱相合性的必要条件是:当n→∞时,S-1n→0。

In this paper,we study the solution βn of quasi-maximum likelihood equation Ln(β)=∑ni=1XiH(X'iβ)Λ-1(X'iβ)(yi-h(X'iβ))=0 for generalized linear models.Under the assumption of an unnatural link function and other some mild conditions,we prove the convergence rate βn-β0≠op(λn-1/2) and necessary conditions is when n→∞,we have S-1n→0.