一般回归模型中的U统计量

U-STATISTICS IN GENERAL REGRESSION MODEL

本文考虑一般回归模型中回归系数的方向的估计问题。一般回归模型的定义中,应变量y在自变量x给定之下的分布只依赖于x之分量的线性组合。这个线性组合的系数向量β就是回归系数向量。一般回归模型是通常线性模型的推广。本文中,我们构造了一个U统计量作为β之方向的估计。在适当的光滑性条件下,本文证明了该U统计量作为β的方向的估计具有相合性与渐近正态性。

In this paper, the estimation of the direction of the regression coefficient of general regression model is considered. According to the definition of general regression model, the conditional distribution of the outcome variable Y depends on X only through a linear combination β'X, where β is the regression coefficient vector of the model. General regression model is a generalization of linear model. In this paper, a series of U-statistics, which is to be the estimator of the direction of vector β, is constructed, and the consistency, asymptotic normality of the series are obtained.