Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors

Abstract

Consider the semiparametric regression model yi = xi β + g (ti) + Vi, 1 ≤ i ≤ n, where β is an unknown parameter of interest, (xi, ti) are nonrandom design points, yi are the response variables, g ({dot operator}) is an unknown function defined on the closed interval [0, 1], and the correlated errors Vi = ∑j = - ∞∞ ψj ei - j, with ∑j = - ∞∞ | ψj |