Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2008.11.01
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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($n^{-1/4}({\log}\;n)^{3/4}$).

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References

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