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

Title & Authors
A BERRY-ESSEEN TYPE BOUND OF REGRESSION ESTIMATOR BASED ON LINEAR PROCESS ERRORS
Liang, Han-Ying; Li, Yu-Yu;

Abstract
Consider the nonparametric regression model $\small{Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}}$ ($\small{1\;{\leq}\;i\;{\leq}\;n}$), where g($\small{\cdot}$) is an unknown regression function, $\small{x_{ni}}$ are known fixed design points, and the correlated errors {$\small{{\epsilon}_{ni}}$, $\small{1\;{\leq}\;i\;{\leq}\;n}$} have the same distribution as {$\small{V_i}$, $\small{1\;{\leq}\;i\;{\leq}\;n}$}, here $\small{V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}}$ with $\small{{\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|}$ < $\small{\infty}$ and {$\small{e_t}$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\small{\cdot}$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($\small{n^{-1/4}({\log}\;n)^{3/4}}$).
Keywords
nonparametric regression model;negatively associated random variable;Berry-Esseen type bound;
Language
English
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