误差不相关广义线性模型极大拟似然估计的收敛速度

Rate of weak consistency of maximum quasi-likelihood estimator in generalized linear models

在广义线性模型(GLM)中,设yi和Zi分别是响应变量和回归系数向量.若随机误差ei=yi-Eyi,i=1,2,…不相关,且sup var(ei)<∞,sup‖Zi‖2<∞,λn→∞和一些光滑条件满足,i≥1i≥1该文证明了一般联系函数GLM回归参数极大拟似然估计βn是弱相合的,具有收敛速度‖β-β0‖=Op(λn-1/2)n),其中λn是i∑i=1ZiZ′的最小特征根,β0是回归参数向量真值.

In a generalized linear model with uncorrelated responses yi, bounded and fixed regressors Zi, and general link function, under assumptions that λn→∞, supvar i≥1（ei）〈∞ and some smoothness conditions, we prove that quasi-likelihood estima tor βn, of regression parameter vector β is weakly consistent with ｜｜β^-β0｜｜=Op（λn-1/2）,where λn is the minimum eigenvalue of ∑i=1^nZiZi＇and β0 is the true value of β.