A universal strong law of large numbers for conditional expectations via nearest neighbors

被引：0

作者：

Walk, Harro ^{[1
]}

机构：

[1] Univ Stuttgart, Fachbereich Math, D-70569 Stuttgart, Germany

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2008年 / 99卷 / 06期

关键词：

conditional expectation; nearest neighbor regression estimation; strong universal pointwise consistency; strong law of large numbers;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For k(n)-nearest neighbor estimates of a regression Y on X (d-dimensional random vector X, integrable real random variable V) based on observed independent copies of (X, Y), strong universal pointwise consistency is shown, i.e., strong consistency P-X-almost everywhere for general distribution of (X, Y). With tie-breaking by indices, this means validity of a universal strong law of large numbers for conditional expectations E(Y\X = x). (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：1035 / 1050

页数：16

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