On the variable bandwidth kernel estimation of conditional U-statistics at optimal rates in sup-norm

• Published in: Physica A Vol. 625; p. 129000
• Main Authors: Bouzebda, Salim, Taachouche, Nourelhouda
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2023; Elsevier
• Subjects: Bias reduction; Empirical process methods; Functional Analysis; Kernel estimation; Machine learning problems; Mathematics; Nonparametric estimation; Probability; Regression-type models; Statistics; Statistics Theory; U-process; U-statistics; Uniform in bandwidth; Variable bandwidth; 62G05; 62G07; 60G10; Nonparametric estimation; Empirical process methods; Kernel estimation; U-process; Machine learning problems; 62H 12; Regression-type models; U-statistics; Bias reduction; Uniform in bandwidth; 60F05; 60G15; Variable bandwidth

U-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every k-tuple of distinct observations of X. W. Stute [Ann. Probab. 19 (1991) 812–825] intr...