Asymptotics of minimum distance estimator in linear regression models under strong mixing

Abstract

Consider the linear model Y_ni = x_niβ+e_ni, i = 1, …, n, where β is the parameter of interest, x_ni's are known constants. Assume that , for each n, {e_ni,…,e_nn} have the same joint distribution as {⊨,…,⊨_n}, where {⊨_t, t= 1,2,…} is a strictly stationary and strong mixing sequence defined on a probability space (Ω,ß, P) and taking values on R. This paper investigates the asymptotic properties of a class of minimum distance Cramer-Von Mises type estimators of the slope parameter in the model. These estimators obtained by minimizing an integrated squared difference between weighted empiricals of the residuals and their expectations with respect to a large class of integrating measures. The estimator _d of β is shown to be asymptotically normal

Keywords:

• asymptotic representation
• asymptotic normality