基于相依数据的非参数回归函数和尺度函数的联立稳健估计

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 835-847.

基于相依数据的非参数回归函数和尺度函数的联立稳健估计

王宏宁^1,2, 俞焕然¹

1. 兰州大学力学系兰州 |730000|2. 甘肃广播电视大学兰州 |730030

收稿日期:2008-12-29 修回日期:2010-03-03 出版日期:2010-05-25 发布日期:2010-05-25

Robust Nonparametric Regression with Simultaneous Scale Curve Estimation Based on Dependent Observations

WANG Hong-Ning^1,2, YU Huan-Ran¹

1. Department of Mechanics, Lanzhou University, Lanzhou 730000|2. Gansu Radio &|TV University, Lanzhou 730030

Received:2008-12-29 Revised:2010-03-03 Online:2010-05-25 Published:2010-05-25

摘要/Abstract

摘要：

该文将Härdle和Tsybakov^{[6, p120-135]}的结果推广到数据来自α -混合的严平稳序列的情形, 得到了估计的相合性和渐近正太性. 在小样本的情形下给出了随机模拟结果, 以检查所提出估计的表现.

关键词: 非参数回归, 稳健曲线估计, 回归曲线和尺度曲线的联立估计, 强混合, 相合性, 渐近正太性

Abstract:

Härdle and Tsybakov's results ([6, p120--135]) is extended to the case where samples are drawn from the strictly stationary sequence with α-mixing. The consistency and asymptotic normality of the estimators are obtained. Simulation studies are conducted to examine the small-sample properties of the proposed estimates.

Key words: Nonparametric regression, Robust curve estimation, Joint estimation of regression and scale curve, Strong mixing, Consistency, Asymptotic normality

中图分类号:

62G05

王宏宁, 俞焕然. 基于相依数据的非参数回归函数和尺度函数的联立稳健估计[J]. 数学物理学报, 2010, 30(3): 835-847.

WANG Hong-Ning, YU Huan-Ran. Robust Nonparametric Regression with Simultaneous Scale Curve Estimation Based on Dependent Observations[J]. Acta mathematica scientia,Series A, 2010, 30(3): 835-847.

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