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

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.

Statistical Inference for Estimators in a Semiparametric EV Model with Linear Process Errors and Missing Responses

“…For example, Miao and Liu [6] obtained the moderate deviation principle for the least squares estimators (LSEs) of the unknown parameters in the model. And Zhang et al [7] studied the asymptotic normality and mean consistency of the least squares estimators (LSEs) in the EV model with dependent errors. We can also fnd more discussions in the work of Liu and Chen [8], Miao et al [9], and Fan et al [1], and so on.…”