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http://dx.doi.org/10.4134/JKMS.2008.45.6.1753

A BERRY-ESSEEN TYPE BOUND OF REGRESSION ESTIMATOR BASED ON LINEAR PROCESS ERRORS  

Liang, Han-Ying (DEPARTMENT OF MATHEMATICS TONGJI UNIVERSITY)
Li, Yu-Yu (DEPARTMENT OF MATHEMATICS TONGJI UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.6, 2008 , pp. 1753-1767 More about this Journal
Abstract
Consider the nonparametric regression model $Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$ ($1\;{\leq}\;i\;{\leq}\;n$), where g($\cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${\epsilon}_{ni}$, $1\;{\leq}\;i\;{\leq}\;n$} have the same distribution as {$V_i$, $1\;{\leq}\;i\;{\leq}\;n$}, here $V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$ with ${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$ < $\infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({\log}\;n)^{3/4}$).
Keywords
nonparametric regression model; negatively associated random variable; Berry-Esseen type bound;
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