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

被引:224
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
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
收藏
页码:1371 / 1385
页数:15
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