Berry–Esseen type bounds in heteroscedastic errors-in-variables model. Issue 13 (2nd July 2016)

• Record Type: Journal Article
• Authors: Zhang, Jing-Jing; Liang, Han-Ying
• Is Part Of: Communications in statistics. Volume 45:Issue 13(2016)
• Page Start: 3993
• Page End: 4017
• Publication Date: 2016-07-02
• Subjects: α-mixing -- Berry–Esseen type bound -- Heteroscedastic -- Least-squares estimator -- Partially linear EV model; 62J12 -- 62E20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.915042
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Consider the heteroscedastic partially linear errors-in-variables (EV) model yi = xi β + g ( ti ) + ε i, ξ i = xi + μ i (1 ⩽ i ⩽ n ), where ε i = σ i ei are random errors with mean zero, σ 2 i = f ( ui ), ( xi, ti, ui ) are non random design points, xi are observed with measurement errors μ i . 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.