Asymptotic normality and mean consistency of LS estimators in the errors-in-variables model with dependent errors

被引：4

作者：

Zhang, Yu ^{[1
]}

Liu, Xinsheng ^{[1
]}

Yu, Yuncai ^{[1
]}

Hu, Hongchang ^{[2
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, State Key Lab Mech & Control Mech Struct, Nanjing, Peoples R China

[2] Hubei Normal Univ, Coll Math & Stat, Huangshi, Hubei, Peoples R China

来源：

OPEN MATHEMATICS | 2020年 / 18卷

基金：

中国国家自然科学基金;

关键词：

errors-in-variables model; negatively superadditive dependent; asymptotic normality; mean consistency; strong law of large numbers; EV REGRESSION-MODEL; NEGATIVE SUPERADDITIVE DEPENDENCE; WEAK CONSISTENCY; COMPLETE CONVERGENCE; ARRAYS;

D O I：

10.1515/math-2020-0052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, an errors-in-variables regression model in which the errors are negatively superadditive dependent (NSD) random variables is studied. First, the Marcinkiewicz-type strong law of large numbers for NSD random variables is established. Then, we use the strong law of large numbers to investigate the asymptotic normality of least square (LS) estimators for the unknown parameters. In addition, the mean consistency of LS estimators for the unknown parameters is also obtained. Some results for independent random variables and negatively associated random variables are extended and improved to the case of NSD setting. At last, two simulations are presented to verify the asymptotic normality and mean consistency of LS estimators in the model.

引用

页码：930 / 947

页数：18

共 29 条

[1] Amini M., 2015, Sib. Adv. Math, V25, P11, DOI [10.3103/S1055134415010022, DOI 10.3103/S1055134415010022]
[2] Strong and weak consistency of least squares estimators in simple linear EV regression models
Chen, Pingyan
Wen, Luliang
Sung, Soo Hak
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2020, 205 : 64 - 73
[3] A connection between supermodular ordering and positive/negative association
Christofides, TC
Vaggelatou, E
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2004, 88 (01) : 138 - 151
[4] PANEL DATA FROM TIME-SERIES OF CROSS-SECTIONS
DEATON, A
[J]. JOURNAL OF ECONOMETRICS, 1985, 30 (1-2) : 109 - 126
[5] Some maximal inequalities for quadratic forms of negative superadditive dependence random variables
Eghbal, N.
Amini, M.
Bozorgnia, A.
[J]. STATISTICS & PROBABILITY LETTERS, 2010, 80 (7-8) : 587 - 591
[6] Asymptotic properties for LS estimators in EV regression model with dependent errors
Fan, Guo-Liang
Liang, Han-Ying
Wang, Jiang-Feng
Xu, Hong-Xia
[J]. ASTA-ADVANCES IN STATISTICAL ANALYSIS, 2010, 94 (01) : 89 - 103
[7] Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms
Fazekas, I
Kukush, AG
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 34 (10) : 23 - 39
[8] Asymptotic normality of DHD estimators in a partially linear model
Hu, Hongchang
Zhang, Yu
Pan, Xiong
[J]. STATISTICAL PAPERS, 2016, 57 (03) : 567 - 587
[9] Hu T.Z., 2000, CHIN J APPL PROBAB S, V16, P133
[10] NEGATIVE ASSOCIATION OF RANDOM-VARIABLES, WITH APPLICATIONS
JOAGDEV, K
PROSCHAN, F
[J]. ANNALS OF STATISTICS, 1983, 11 (01) : 286 - 295

← 1 2 3 →