Exponential probability inequality for m-END random variables and its applications

被引：0

作者：

Wang, Xuejun ^{[1
]}

Wu, Yi ^{[1
]}

Hu, Shuhe ^{[1
]}

机构：

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

来源：

METRIKA | 2016年 / 79卷 / 02期

基金：

中国国家自然科学基金;

关键词：

m-extended negatively dependent random variables; Complete convergence; Kolmogorov exponential inequality; Complete consistency; DEPENDENT RANDOM-VARIABLES; NONPARAMETRIC MULTIPLE-REGRESSION; PRECISE LARGE DEVIATIONS; FIXED-DESIGN REGRESSION; COMPLETE CONVERGENCE; ARRAYS; SUMS;

D O I：

10.1007/s00184-015-0547-7

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：

The concept of m-extended negatively dependent (m-END, in short) random variables is introduced and the Kolmogorov exponential inequality for m-END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise m-END random variables and the complete consistency for the estimator of nonparametric regression models based on m-END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables.

引用

页码：127 / 147

页数：21

共 31 条

[1] ON COMPLETE CONVERGENCE FOR ARRAYS OF ROW-WISE NEGATIVELY ASSOCIATED RANDOM VARIABLES
Chen, P.
Hu, T. -C.
Liu, X.
Volodin, A.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2008, 52 (02) : 323 - U6
[2] THE STRONG LAW OF LARGE NUMBERS FOR EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES
Chen, Yiqing
Chen, Anyue
Ng, Kai W.
[J]. JOURNAL OF APPLIED PROBABILITY, 2010, 47 (04) : 908 - 922
[3] CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION FOR DEPENDENT HETEROGENEOUS PROCESSES - THE FIXED DESIGN CASE
FAN, Y
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1990, 33 (01) : 72 - 88
[4] Georgiev A.A., 1983, MATH STAT APPL, VB, P141
[5] CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION - THE FIXED DESIGN CASE
GEORGIEV, AA
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1988, 25 (01) : 100 - 110
[6] COMPLETE CONVERGENCE AND THE LAW OF LARGE NUMBERS
HSU, PL
ROBBINS, H
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1947, 33 (02) : 25 - 31
[7] Fixed-design regression for linear time series
Hu, SH
Zhu, CH
Chen, YB
Wang, LC
[J]. ACTA MATHEMATICA SCIENTIA, 2002, 22 (01) : 9 - 18
[8] A note on complete convergence for arrays
Hu, TC
Szynal, D
Volodin, AI
[J]. STATISTICS & PROBABILITY LETTERS, 1998, 38 (01) : 27 - 31
[9] On complete convergence for arrays of rowwise m-negatively associated random variables
Hu, Tien-Chung
Chiang, Chen-Yu
Taylor, Robert L.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : E1075 - E1081
[10] On complete convergence for arrays
Kruglov, Victor M.
Volodin, Andrei I.
Hu, Tien-Chung
[J]. STATISTICS & PROBABILITY LETTERS, 2006, 76 (15) : 1631 - 1640

← 1 2 3 4 →