半参数回归模型的二阶段局部推断

Two-stage Local Inference for a Class of Semiparamtric Regression Model

本文在随机设计情形下考虑一类半参数回归模型：Y=X^Tβ+g(T)+e,其中Y为响应变量,X为s×n设计矩阵,β为一s×1未知向量,g(?)是未知函数．本文在迭代机制上利用了一类局部核权对数似然估计法及二阶段法分别给出了参数部分β和非参数部分g(?)的估计量(?)和(?)(?),讨论了其相关属性．就n^(1/2)(?)的渐近正态性及(?)的收敛性而言,我们已经证明：只要参数部分β的初始估计(?)较好,本文所用的二阶段法能达到其它方法的效果,如逐点多项式逼近法,核与最小二乘法和最近邻与最小二乘法,等等．

Consider a class of semiparametric regression model under random design Y=X^Tβ＋g（T）＋e,where the s x1 vector β is unknown. Y is a response vector, X an s x n design matrix, and g（·） an unknown function. Using techniques called the local kernel weighted log-likelihood and the second stage local inference, the estimators β^^ and g^^（·） of the parametric part ~ and the nonpaxametric part g（·） reapectively are obtained on the basis of the iterative device for the system. Properties of the estimators are discussed. We demonstrate that as long as initial estimators for the parametric part are reasonably good, the techniques used here perform at least as well as the same roles as those exiting methods in the case of the asymptotical normality of √（β^^-β） and the convergency of g^^（·）.