Asymptotics of estimators in semi-parametric model under NA samples

Abstract

This paper is concerned with the heteroscedastic semi-parametric regression model y i = x i β + g ( t i ) + σ i e i , 1 ⩽ i ⩽ n , where σ i 2 = f ( u i ) , ( x i , t i , u i ) are fixed design points, g and f are unknown functions, and random errors e i are negatively associated (NA) random variables. The strong consistency and asymptotic normality for least-squares estimators and weighted least-squares estimators of β are studied. In addition, the strong consistency for the estimators of f ( · ) and g ( · ) is investigated. Some results on independent random error settings are extended.