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

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  • Jing-Jing Zhang
  • Han-Ying Liang

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.

Suggested Citation

  • Jing-Jing Zhang & Han-Ying Liang, 2016. "Berry–Esseen type bounds in heteroscedastic errors-in-variables model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3993-4017, July.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:13:p:3993-4017
    DOI: 10.1080/03610926.2014.915042
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