Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data

Salim Bouzebda (), Thouria El-hadjali () and Anouar Abdeldjaoued Ferfache ()
Additional contact information
Salim Bouzebda: Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne)
Thouria El-hadjali: Université Frères Mentouri
Anouar Abdeldjaoued Ferfache: Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne)

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 17, 1548-1606

Abstract: Abstract U-statistics represent a fundamental class of statistics from modelling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of Stute (Ann. Probab. 19, 812–825 1991) introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r ( t ) : = E [ φ ( Y 1 , … , Y m ) | ( X 1 , … , X m ) = t ] , for t ∈ ℝ d m . $$r(\mathbf{ t}):=\mathbb{E}[\varphi(Y_{1},\ldots,Y_{m})|(X_{1},\ldots,X_{m})=\mathbf{t}], ~~\text{for}~~\mathbf{ t}\in \mathbb{R}^{dm}.$$ We apply the methods developed in Dony and Mason (Bernoulli 14(4), 1108–1133 2008) to establish uniform in t and in bandwidth consistency (i.e., h, h ∈ [an,bn] where 0

Keywords: Non-parametric estimation; regression; conditional empirical processes; conditional U-processes; kernel estimation; functional estimation; VC-classes.; Primary 60F05, 60G15, 60G10, 62G08, 62G07; Secondary 62G15, 62G30 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-022-00301-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00301-7

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-022-00301-7

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().