线性约束下部分线性模型中估计的渐近性质  

Asymptotic Properties of Estimatiors in Partially Linear Models Under Linear Restriction

作　　者：李晨[1] 余波[1] 刘万荣[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《数学理论与应用》2005年第1期91-94,共4页Mathematical Theory and Applications

摘　　要：考虑回归模型yi=x′iβ+ g(ti) + ei, 0 ≤i ≤nr=Rβ其中(xi,ti)是固定非随机设计点列,xi=(xi1,…,xip)′,β=(β1,…,βp)′(p 1) ,g是定义在[0 ,1]上的未知函数,β是未知待估参数,0≤ ti≤1i,ei 是i.i.d随机误差,且Eei=0 ,Ee2i=σ2 <∞.r是一个J维向量,R是一个J* p列满秩矩阵,基于g的估计取一个非参数权估计,本文讨论了在线性约束下β的最小二乘估计的相合性及渐近正态性.Consider the following regression models y_i=x′_iβ+g(t_i)+e_i, 0in r=Rβ where (x_i,t_i) are fixed and nonrandom design points x_i=(x_ i1,...,x_ ip)′,β=(β_1,...,β_p)′(p1),g(.) is an unkown function over ,β is a unknown parameter to be estimated,0t_i1_i,e_i(i=1,...,n) are i.i.d random error with Ee_i=0,Ee^2_i=σ~2<∞.And r is a J-vector ,R is a J~* K-matrix which is full rank in column. Based on g estimated by the family of nonparametric estimates,the consistency and asymptotic normality of least-square of β are dicussed.

关 键 词：部分线性模型 线性约束 渐近性质 满秩矩阵 未知函数 相合性 估计 固定 β1 随机设计 

分 类 号：O212.1[理学—概率论与数理统计]