Berry–Esseen type bounds in heteroscedastic errors-in-variables model

Abstract

ABSTRACTConsider the heteroscedastic partially linear errors-in-variables (EV) model yi = xiβ + g(ti) + εi, ξi = xi + μi (1 ⩽ i ⩽ n), where εi = σiei are random errors with mean zero, σ2i = f(ui), (xi, ti, ui) are non random design points, xi are observed with measurement errors μi. When f( · ) is known, we derive the Berry–Esseen type bounds for estimators of β and g( · ) under {ei, 1 ⩽ i ⩽ n} is a sequence of stationary α-mixing random variables, when f( · ) is unknown, the Berry–Esseen type bounds for estimators of β, g( · ), and f( · ) are discussed under independent errors.