On the uniform-in-bandwidth consistency of the general conditional U-statistics based on the copula representation. Issue 2 (3rd April 2021)

• Record Type: Journal Article
• Authors: Bouzebda, Salim; Elhattab, Issam; Nemouchi, Boutheina
• Is Part Of: Journal of nonparametric statistics. Volume 33:Issue 2(2021)
• Page Start: 321
• Page End: 358
• Publication Date: 2021-04-03
• Subjects: Conditional U-statistics -- data-dependent bandwidth selection -- empirical process -- uniform-in-bandwidth -- copula regression function; 62G07 -- 60F05 -- 60F15 -- 62E20 -- 62G30; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2021.1937621
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : Stute [Ann. Probab. 19 (1991) 812–825] introduced a class of estimators called conditional U -statistics of 1 E ( φ ( Y 1, …, Y m ) ∣ ( X 1, …, X m ) = t ), for t ∈ R m . In the present work, we provide a new class of estimators of conditional U -statistics. More precisely, we investigate the conditional U -statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. Our theorems allow data-driven local bandwidths for these statistics. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in copula regression analysis. The performance of these procedures is evaluated through simulation in the context of the conditional Kendall's tau.