最近邻估计在任意紧集上一致强收敛速度
Rates of Strong Uniform Convergence of Nearest Neighbor Density Estimates on Any Compact Set
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摘要: 在这篇文章中,我们提出了最近邻估计在任意紧集上一致强收敛速度的概念,得到了一些较好的收敛速度.因此,最近邻估计的逐点强收敛速度问题是本文的特例,扩大了最近邻估计的应用范围.Abstract: In this paper, we propose the concept of rates of strong uniform convergence of nearest neighbor density estimates on any compact set and obtain some better convergence rates. Hence the problem of the strong uniform convergence rates predetermined is its special example. The applied region of the estimate is extended.
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[1] Wagner,T.J.,Strong consistency of a nonparametric estimate of a density function,IEEE Transaction on Systems Man and Cybernetics,3(1973).289-290. [2] 陈希孺,最近邻密度估计的收敛速度,中国科学,A辑.12 (1981), 1419-1428. [3] 白志东,最近邻密度估计的中心极限定理.中国科技大学学报,5 (1983), 114-118. [4] 卢江,最近邻密度估计的逐点强收敛速度,应用概率统计.2, 1 (1988), 21-27. [5] Chung,K.L.,An estimate concerning the Kolmogoroff limit distribution,Trans.Amer.Math.Soc.,67(1949),36-50. [6] Devroye,L.P.and T.J.Wagner,The strong uniform consistency of kernel density estimates,Multivariate Analysis.5(1980),59-77. -
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