部分线性模型中估计的渐近正态性

Asymptotic Normality of a Class of Estimators in Partial Linear Models

考虑回归模型其中是未知函数，（ｘ＿ｉ，ｔ＿ｉ，ｕ＿ｉ）是固定非随机设计点列，β是待估参数，ｅ＿ｉ是随机误差。基于ｇ（·）及ｆ（·）的一类非参数估计（包括常见的核估计和近邻估计），我们构造了β的加权最小二乘估计，并证得了最小二乘估计和加权最小二乘估计的渐近正态性。

Consider the heteroscedastic regression,model y_i=x_iβ+g(t_i)+σ_ie_i forand i=1,2,…,n. Here the design points (x_i,t_i,u_i)are known and nonrandom,g and f areunknown functions, and e_i is an unobserued disturbahce. The family of nonparametric estimatesand including all known estimates is proposed,also proposed is a class of new nearestneighbor estimates of g and f.The least squares estimator β_n and the weighted least squaresestimator are obtained. Some asymptotically efficient estimates are also obtained.