Least square estimators in linear regression models under negatively superadditive dependent random observations

TL;DR

This paper investigates the strong consistency and convergence rate of least squares estimators in linear regression models with negatively superadditive dependent random observations, under mild moment and dependence assumptions.

Contribution

It introduces conditions for strong consistency of least squares estimators with negatively superadditive dependent data and analyzes their convergence rate.

Findings

Estimator is strongly consistent under mild assumptions.

Convergence rate is proportional to sampling rate N.

Simulation study illustrates finite sample properties.

Abstract

In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced observations and the residuals under which the estimator is strongly consistent. In particular, we consider observation instances that are negatively superadditive dependent within each other, while for the residuals we merely assume that they are generated by some continuous function. In addition, we prove that the rate of convergence is proportional to the sampling rate $N$, and we complement our findings with a simulation study providing insights on finite sample properties.