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| Almost Sure Convergence of Nonparametric Begression Estimates |
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Citation： |
Chen Xiru.Almost Sure Convergence of Nonparametric Begression Estimates[J].Chinese Annals of Mathematics B,1985,6(1):103~108 |
| Page view： 698
Net amount： 966 |
Authors： |
Chen Xiru; |
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| Abstract： |
Let (X, Y), (X_i,Y_i), i=1,\cdots, n, be iid.R^d*R^1-ralued vandom vectors with
E(|Y|) <\infinity and m(x) =E(Y|X=x) be the regression function. Select the weight functions W_ni(x) =W_ni(x; X_1,\cdots, X_n), and use m_n(x) =[\sum\limits_{i = 1}^n {{W_{ni}}(x){Y_i}} \] an estimator of m(x). This paper shows that [\mathop {\lim }\limits_{n \to \infty } \]m_n(X) =m(X), a. s., under weaker conditions. |
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