部分线性模型中非参数估计的强相合性

Strong Consistency of a Class of Nonparametric Estimators in Partial Linear Model

考虑部分线性模型:y_i=x_iβ+g(t_i)+σ_ie_i,1≤i≤n,其中σ_i^2=f(u_i),(x_i,t_i,u_i)是固定非随机设计点列,f(·)和 g(·)是未知函数,β是待估参数,e_i 是随机误差。我们研究了基于β的最小二乘估计β_n 和加权最小二乘估计_n 的非参数 g(·)的估计,并证明了他们的强相合性。

Consider the partial linear model :y_i=x_iβ+g(t_i)+σ_ie_i,1≤i≤n,where σ_i^2=f(u_i),Here the design points(x_i,t_i,u_i)are known and nonrandom,g and f are unknown functions,and e_iis an unob- served disturbance.We study the estimators of nonparametric g(·)based on the least squares estimator _n and the weighted least squares estimator_nof β,and establish their strong consistency.