Strong laws for weighted sums of widely orthant dependent random variables and applications

被引：0

作者：

Zhu, Yong ^{[1
]}

Wang, Wei ^{[1
]}

Chen, Kan ^{[2
]}

机构：

[1] Chizhou Univ, Sch Big Data & Artificial Intelligence, Chizhou 247000, Peoples R China

[2] Chaohu Univ, Sch Math & Stat, Chaohu 238024, Peoples R China

来源：

OPEN MATHEMATICS | 2024年 / 22卷 / 01期

关键词：

strong law of large numbers; weighted sums; widely orthant dependent; strong consistency; FIXED-DESIGN REGRESSION; STRONG CONSISTENCY; ASYMPTOTIC UNBIASEDNESS; CONVERGENCE; ESTIMATOR; MODEL;

D O I：

10.1515/math-2024-0027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

引用

页数：14

共 37 条

[1] STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN NORMAL LINEAR-REGRESSION
ANDERSON, TW
TAYLOR, JB
[J]. ANNALS OF STATISTICS, 1976, 4 (04) : 788 - 790
[2] CONSISTENCY, ASYMPTOTIC UNBIASEDNESS AND BOUNDS ON THE BIAS OF S(2) IN THE LINEAR-REGRESSION MODEL WITH ERROR COMPONENT DISTURBANCES
BALTAGI, BH
KRAMER, W
[J]. STATISTICAL PAPERS, 1994, 35 (04) : 323 - 328
[3] Further Spitzer's law for widely orthant dependent random variables
Chen, Pingyan
Luo, Jingjing
Sung, Soo Hak
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2021, 2021 (01)
[4] Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models
Chen, Yang
Wang, Le
Wang, Yuebao
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 401 (01) : 114 - 129
[5] Strong consistency of least squares estimates with i.i.d. errors with mean values not necessarily defined
da Silva, Joao Lita
Mexia, Joao Tiago
[J]. STATISTICS, 2013, 47 (04) : 707 - 714
[6] WEAK AND STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATORS IN REGRESSION MODELS
DRYGAS, H
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1976, 34 (02): : 119 - 127
[7] CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION FOR DEPENDENT HETEROGENEOUS PROCESSES - THE FIXED DESIGN CASE
FAN, Y
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1990, 33 (01) : 72 - 88
[8] Georgiev A. A., 1985, Local properties of function fitting estimates with applications to system identification, ppp. 141
[9] CONVERGENCE SYSTEMS AND STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN REGRESSION-MODELS
GUIJING, C
LAI, TL
WEI, CZ
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1981, 11 (03) : 319 - 333
[10] Fixed-design regression for linear time series
Hu, SH
Zhu, CH
Chen, YB
Wang, LC
[J]. ACTA MATHEMATICA SCIENTIA, 2002, 22 (01) : 9 - 18

← 1 2 3 4 →