The consistency for the estimator of nonparametric regression model based on martingale difference errors

被引：29

作者：

Chen, Zhiyong ^{[1
]}

Wang, Haibin ^{[1
]}

Wang, Xuejun ^{[2
,3
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

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

[3] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

STATISTICAL PAPERS | 2016年 / 57卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Martingale difference sequence; Mean consistency; Complete consistency; Strong consistency; Nearest neighbor weights; DEPENDENT RANDOM-VARIABLES; COMPLETE CONVERGENCE; MULTIPLE-REGRESSION; SEQUENCES;

D O I：

10.1007/s00362-015-0662-6

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, by using the inequalities for martingale difference sequence, we investigate the consistency for the estimator of nonparametric regression model based on martingale difference errors. Some results on consistency for the estimator of are presented, including the mean consistency, complete consistency and strong consistency. As an application, the consistency for the nearest neighbor estimator is obtained.

引用

页码：451 / 469

页数：19

共 33 条

[1] ASYMPTOTIC DISTRIBUTIONS OF REGRESSION AND AUTOREGRESSION COEFFICIENTS WITH MARTINGALE DIFFERENCE DISTURBANCES [J].

ANDERSON, TW ;

KUNITOMO, N .

JOURNAL OF MULTIVARIATE ANALYSIS, 1992, 40 (02) :221-243

[2] When bubbles burst: econometric tests based on structural breaks [J].

Breitung, Joerg ;

Kruse, Robinson .

STATISTICAL PAPERS, 2013, 54 (04) :911-930

[3]

[陈平炎 Chen Pingyan], 2011, [数学物理学报. A辑, Acta Mathematica Scientia], V31, P179

[4] CONVERGENCE OF SUMS OF SQUARES OF MARTINGALE DIFFERENCES [J].

CHOW, YS .

ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (01) :123-&

[5]

DEDECKER J, 2008, SOC IND APPL MATH, V50, P416

[6]

Elton J, 2012, ANN PROBAB, V1981, P405

[7] CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION FOR DEPENDENT HETEROGENEOUS PROCESSES - THE FIXED DESIGN CASE [J].

FAN, Y .

JOURNAL OF MULTIVARIATE ANALYSIS, 1990, 33 (01) :72-88

[8]

Georgiev A. A., 1983, MATH STAT APPL B, P141

[9] NONPARAMETRIC FUNCTION RECOVERING FROM NOISY OBSERVATIONS [J].

GEORGIEV, AA ;

GREBLICKI, W .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1986, 13 (01) :1-14

[10] CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION - THE FIXED DESIGN CASE [J].

GEORGIEV, AA .

JOURNAL OF MULTIVARIATE ANALYSIS, 1988, 25 (01) :100-110

← 1 2 3 4 →