韦来生,苏淳.非参数回归函数最近邻估计Lp收敛的速度(英文)[J].数学研究及应用,1986,6(2):117~123
非参数回归函数最近邻估计Lp收敛的速度(英文)
On the Pointwisise Lp Convergence Rates of Nearest Neighbor Estimate of Nonparametric Regression Function
投稿时间:1983-01-31  
DOI:10.3770/j.issn:1000-341X.1986.02.026
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韦来生 中国科技大学 
苏淳 中国科技大学 
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      Let (X,Y) be a Rd×R1-valued random vector with E(|Y|)<∞,m(x)=E(Y|X=x) be the regression funvion of Y with respect to X.Suppose that (Xi, Yi),i=1, …,n, are iid samples drawn from (X,Y). It is desired to estimate m(x) based on these samples,everoye discussed in 1981 (see [2]) the pointwise Lp-convergence of the nearest neigthoor estimate mn(x) (see (5) of the present paper). In this article we further study the rate of this convergence.It is shown that if there exists p≥2 such that E |Y|p<∞,then E|mn(x)-m(x)|p=O(n-p/(d+2))a.s. for suitabte choice of the weighte Cm (see(4) of the present paper).
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