Asymptotic normality and mean consistency for the weighted estimator in nonparametric regression models

被引：2

作者：

Wu, Yi ^{[1
]}

Wang, Xuejun ^{[1
]}

Sung, Soo Hak ^{[2
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China

[2] Pai Chai Univ, Dept Appl Math, Taejon 302735, South Korea

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2019年 / 48卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Asymptotic normality; Mean consistency; Linearly negative quadrant dependent random variables; Nonparametric regression model; Weighted estimator; FIXED-DESIGN REGRESSION; RANDOM-VARIABLES; COMPLETE CONVERGENCE; SUMS; THEOREM;

D O I：

10.1016/j.jkss.2019.01.004

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we mainly study the asymptotic properties of weighted estimator for the nonparametric regression model based on linearly negative quadrant dependent (LNQD, for short) errors. We obtain the rate of uniformly asymptotic normality of the weighted estimator which is nearly O(n(-1/4)) when the moment condition is appropriate. The results generalize the corresponding ones of Yang (2003) from NA samples to LNQD samples and improve or extend the corresponding one of Li et al. (2012) for LNQD samples. Moreover, we obtain some results on mean consistency, uniformly mean consistency, and the rate of mean consistency for the weighted estimator. Finally we carry out some simulations to verify the validity of our results. (C) 2019 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

引用

页码：463 / 479

页数：17

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