Asymptotic normality and mean consistency of LS estimators in the errors-in-variables model with dependent errors-Reference-Cited by-同舟云学术

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

Published:2020-01-01 Issue:1 Volume:18 Page:930-947
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Zhang Yu¹,Liu Xinsheng¹,Yu Yuncai¹,Hu Hongchang²

Affiliation:

1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics , Nanjing , China

2. College of Mathematics and Statistics, Hubei Normal University, Huangshi , China

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0052/pdf

Reference29 articles.

1. A. Deaton, Panel data from a time series of cross-sections, J. Econ. 30 (1985), 109–126.

2. J. X. Liu and X. R. Chen, Consistency of LS estimator in simple linear EV regression models, Acta Math. Sci. B 25 (2005), 50–58.

3. P. Y. Chen, L. L. Wen, and S. H. Sung, Strong and weak consistency of least squares estimators in simple linear EV regression models, J. Statist. Plann. Inference 205 (2020), 64–73, 10.1016/j.jspi.2019.06.004.

4. Y. Miao, G. Y. Yang, and L. M. Shen, The central limit theorem for LS estimator in simple linear EV regression models, Commun. Stat. Theory Methods 36 (2007), 2263–2272.

5. S. F. Xu and N. Li, Consistency for the LS estimator in the linear EV regression model with replicate observations, J. Korean Statist. Soc. 42 (2013), no. 4, 451–458.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Complete convergence and complete moment convergence for weighted sums of random variables satisfying generalized Rosenthal type inequalities and an application;Stochastics;2024-01

2. On a class of linear regression methods;Journal of Complexity;2024-01

3. Statistical Inference for Estimators in a Semiparametric EV Model with Linear Process Errors and Missing Responses;Mathematical Problems in Engineering;2023-04-20