非参数回归函数的置信区间

应用科学学报 ›› 2002, Vol. 20 ›› Issue (1): 77-79.

非参数回归函数的置信区间

薛留根

北京工业大学应用数理学院, 北京 100022

收稿日期:2000-06-22 修回日期:2001-06-02 出版日期:2002-03-31 发布日期:2002-03-31
作者简介:薛留根(1957-),男,河南鄢陵人,教授,博导.
基金资助:
北京市自然科学基金资助项目(1992005);国家教育部骨干教师资助计划资助项目

The Confidence Intervals of the Nonparametric Regression Function

XUE Liu-gen

College of Applied Sciences, Beijing Polytechnic University, Beijing 100022, China

Received:2000-06-22 Revised:2001-06-02 Online:2002-03-31 Published:2002-03-31

摘要/Abstract

摘要： 利用随机加权法构造非参数回归函数的随机加权统计量,证明了用随机加权统计量的分布去逼近原估计量的误差分布,其精度可达到o(n^-1/(d+2) lnnM_n),a.s.,其中0<M_n→∞.该结果可以用于构造未知回归函数m(x)的置信区间.

关键词: 核估计, 随机加权法, 非参数回归函数

Abstract: In the paper, we apply random weighting methods to construct random weighting statistic for the unknown regression function m(x) and prove that the random weighting approximation can attain the accuracy of o(n^-1/(d+2) lnnM_n),where 0< M_n→∞. The confidence intervals of m(x) can be constructed by this result.

Key words: nonparametric regression function, kernel estimation, random weighting method

中图分类号:

O212.7

薛留根. 非参数回归函数的置信区间[J]. 应用科学学报, 2002, 20(1): 77-79.

XUE Liu-gen. The Confidence Intervals of the Nonparametric Regression Function[J]. Journal of Applied Sciences, 2002, 20(1): 77-79.