非参数回归函数的k_n近邻估计的渐近性质及其Bootstrap逼近  

ASYMPTOTIC PROPERTIES AND BOOTSTRAP APPROXIMATION OF k_n-NEREST NEIGHBOR ESTIMATES OF REGRESSION FUNCTION

作　　者：王炳章[1] 

机构地区：[1]烟台大学数学与信息科学系,烟台264005

出　　处：《应用数学学报》2001年第3期410-417,共8页Acta Mathematicae Applicatae Sinica

摘　　要：本文研究回归函数的ｋｎ－近邻估计的渐近性质，得到了回归函数的ｋｎ－近邻估计的渐近正态性和它的Ｂｏｏｔｓｔｒａｐ统计量的相合性. 在高阶矩存在的条件下，我们证明了回归函数的ｋｎ－近邻估计的Ｂｏｏｔｓｔｒａｐ逼近比正态逼近更精确．In this paper, asymptotic properties of kn-nearest neighbor estimator of reg ression function are investigated, its asymptotic normality and Bootstrap consistency are obtained. Under the condition that higher-order moments are existed, we prove that Boot strap approximation of the kn-nearest neighbor estimator of regression function is more presise than normal approximation.

关 键 词：回归函数 kn-近邻估计 渐近正态性 BOOTSTRAP逼近 Bootstrap统计量 随机向量 

分 类 号：O212.1[理学—概率论与数理统计]