摘要
考虑回归模型 :yi=xiβ+g(ti) +σiei,1≤ i≤ n.其中 σ2i=f(ui) ,(xi,ti,ui)是固定非随机设计点列 ,f (· )和 g(· )是未知函数 ,β是待估参数 ,ei 是随机误差 .对文 [1 ]给出的基于 g(· )及 f(· )的一类非参数估计的β的最小二乘估计β^ n和加权最小二乘估计βn,本文通过重抽样的方法构造了 β^n 和 βn 的 Bootstrap统计量 β^ *n 和 β*n .证明了在给定原样本的条件下 ,n (β^ *n -β^ n)和 n (β*n -β^ n)分别与 n (β^ n-β)和 n (βn-β)有相同的渐近分布 .
Consider the heteroscedastic regression model: y i=x iβ+g(t i)+σ ie i, 1≤i≤n , where σ 2 i= f(u i) , Here the design points (x i, t i, u i) are known and nonrandom, g(·) and f(·) are unknown functions, β is an unknown parameter, and e i is an unobserved disturbance. For the least squares estimator n and the weighted least squares estimator n of β given in based on the family of nonparametric estimates of g(·) and f(·) , we use the resampling method to establish the bootstrap statistic β^ * n for β^ n and β * n for β n, and then prove that under the given original sample the asymptotic distributions of n(β^ * n-β^ n) and n(β * n-β^ n) are same as the ones of n(β^ n-β) and n(β n-β) , respectively.
出处
《数学杂志》
CSCD
北大核心
2002年第3期301-308,共8页
Journal of Mathematics
基金
安徽省教委自然科学基金资助课题
