Facultade de Fisioterapia

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

Zhang, J.J.; Liang, Han-Ying
Abstract:
Consider 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.
Year:
2016
Type of Publication:
Article
Journal:
Communications in Statistics - Theory and Methods
Volume:
45
Number:
13
Pages:
3993-4017
Month:
July
DOI:
https://doi.org/10.1080/03610926.2014.915042
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