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.

Keywords

• errors-in-variables model
• negatively superadditive dependent
• asymptotic normality
• mean consistency
• strong law of large numbers
• 62f12
• 60f05
• 62e20
• 62j05