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

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. We complement our findings with a simulation study providing insights on finite sample properties.