ON THE STRONG UNIVERSAL CONSISTENCY OF NEAREST-NEIGHBOR REGRESSION FUNCTION ESTIMATES

被引：206

作者：

DEVROYE, L

GYORFI, L

KRZYZAK, A

LUGOSI, G

机构：

[1] CONCORDIA UNIV,DEPT COMP SCI,MONTREAL,PQ H3G 1M8,CANADA

[2] TECH UNIV BUDAPEST,DEPT MATH,H-1521 BUDAPEST,HUNGARY

来源：

ANNALS OF STATISTICS | 1994年 / 22卷 / 03期

关键词：

REGRESSION FUNCTION; NONPARAMETRIC ESTIMATION; CONSISTENCY; STRONG CONVERGENCE; NEAREST NEIGHBOR ESTIMATE;

D O I：

10.1214/aos/1176325633

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：

Two results are presented concerning the consistency of the k-nearest neighbor regression estimate. We show that all modes of convergence in L(1) (in probability, almost sure, complete) are equivalent if the regression variable is bounded. Under the additional condition k/log n --> infinity we also obtain the strong universal consistency of the estimate.

引用

页码：1371 / 1385

页数：15

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