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| Strong Convergence of the Kernel Estimates of Nonparametric Regression Functions |
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Citation： |
Zhao Lincheng,Fang Zhaoben.Strong Convergence of the Kernel Estimates of Nonparametric Regression Functions[J].Chinese Annals of Mathematics B,1985,6(2):147~156 |
| Page view： 872
Net amount： 706 |
Authors： |
Zhao Lincheng; Fang Zhaoben |
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| Abstract： |
Let (X, Y), (X_1, Y_1),\cdots, (X_n, Y_n) be i. i. d. random vectors taking values in R_d\times R with E(|Y|)<\infinity, To estimate the regression function m(x)=E(Y|X=x), we use the kernel estimate $m_n(x)=[\sum\limits_{i = 1}^n {K(\frac{{{X_i} - x}}{{{h_n}}}){Y_i}/} \sum\limits_{i = 1}^n {K(\frac{{{X_j} - x}}{{{h_n}}})} \]$ where K(x) is a kernel function and h_n a window width. In this paper, we establish the strong consistency of m_n(x) when E(|Y|^p)<\infinity for some p>l or E{exp(t|Y|^\lambda)}<\infinity for some \lambda>0 and t>0. It is remakable that other conditions imposed here are independent of the distribution of (X, Y). |
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