广义线性模型中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自然联系情形下的拟似然方程∑ni=1XiH X′iβΛX′iβyi-h X′iβ=0的解β^n.在λ-n→∞和其他一些正则性条件下证明了拟似然方程解β^n的弱相合性,并得到了与自然联系情形下一样的收敛速度,即β^n-β0=Opλ-n-1/2,其中β0为β的真值,λ-n(λ-n)表示方阵Sn=∑ni=1XiX′i的最小(最大)特征值.

In this paper, we study the solutionS, of quasi-maximum likelihood equation n∑XiH（X′β）∧（X′iβ）（yi-h（x′iβ））=0 for generalized linear models （GLMs） , Under the assumption an unnatural link function and other some mild conditions , we prover the weak consistency of the solution βn to the above equation and present its convergence rate, which is as the same as under the natural link condition, that is βn-β0=Op（λn^-1/2）, where β0is the true value of parameterβ and λn （λn）denotes the smallest eigervalue of thematrixSn=n∑i=1 XiXi.