Estimation of a regular conditional functional by conditional U-statistic regression

Alexis Derumigny*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable (Formula presented.) to sums over every (Formula presented.) -tuple of distinct observations of (Formula presented.). They may be used to estimate a regular functional (Formula presented.) of the law of (Formula presented.). When a vector of covariates (Formula presented.) is available, a conditional U-statistic describes the effect of (Formula presented.) on the conditional law of (Formula presented.) given (Formula presented.), by estimating a regular conditional functional (Formula presented.). We state nonasymptotic bounds of general conditional U-statistics and study their asymptotics too. Assuming a parametric model of the conditional functional of interest, we propose a regression-type estimator based on conditional U-statistics. Its theoretical properties are derived, first in a nonasymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods.

Original languageEnglish
Article numbere12350
Number of pages41
JournalStatistica Neerlandica
Volume79
Issue number1
DOIs
Publication statusPublished - 2024

Keywords

  • conditional distribution
  • penalized regression
  • regression-type models
  • U-statistics

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