EconPapers    
Economics at your fingertips  
 

Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences

Salim Bouzebda (salim.bouzebda@utc.fr), Amel Nezzal and Tarek Zari
Additional contact information
Salim Bouzebda: LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, 57 Avenue de Landshut CS 60319, CEDEX, 60203 Compiegne, France
Amel Nezzal: LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, 57 Avenue de Landshut CS 60319, CEDEX, 60203 Compiegne, France
Tarek Zari: Laboratory MAEGE, FSJES Ain-Sebaa, University Hassan II, Casablanca 20000-20200, Morocco

Mathematics, 2022, vol. 11, issue 1, 1-39

Abstract: U -statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U -statistics make generalizations the empirical mean of a random variable X to the sum of all k -tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.

Keywords: nonparametric estimation; regression-type models; U -statistics; conditional distribution; functional estimation; delta sequences; kernel estimation; machine learning problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/1/161/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/1/161/ (text/html)

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:gam:jmathe:v:11:y:2022:i:1:p:161-:d:1018167

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager (indexing@mdpi.com).

 
Page updated 2024-12-28
Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:161-:d:1018167