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

• 成果类型: Article
• 署名作者: DEVROYE, L; GYORFI, L; KRZYZAK, A; LUGOSI, G
• 署名单位: Concordia University - Canada; Budapest University of Technology & Economics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325633
• 发表日期: 1994
• 页码: 1371-1385
• 关键词: Nonparametric regression; CONVERGENCE; density; CLASSIFICATION; EQUIVALENCE; weak; L1

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.