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 language | English |
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Article number | e12350 |
Number of pages | 41 |
Journal | Statistica Neerlandica |
Volume | 79 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2024 |
Keywords
- conditional distribution
- penalized regression
- regression-type models
- U-statistics