Berry–Esseen type bounds in heteroscedastic errors-in-variables model
Berry–Esseen type bounds in heteroscedastic errors-in-variables model
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DOI：
10.1080/03610926.2014.915042
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Jing-Jing Zhang-Jing;Han-Ying Liang
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文献类型：
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作者：
Jing-Jing Zhang-Jing;Han-Ying Liang
考虑异方差部分线性变量误差模型yi=xiβ+g(Ti)+εi，ξi=xi+μi(1⩽i⩽n)，其中εi=σiei是均值为零的随机误差，σ2i=f(Ui)，(xi，ti，ui)是非随机设计点，xi是带有测量误差的μi。当f(·)已知时，我们得到了{Ei，1⩽i⩽n}下α和g(·)的估计量的Berry-Essaw型界，当f(·)未知时，在独立误差下讨论了β、g(·)和f(·)估计的Berry-Esseen型界。
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.