2019/03/26 by Alexis Derumigny, Derumigny, Alexis · 2 citations
Computer Science · Mathematics · #62F12 #62G05 #62J99 #Bayesian Methods and Mixture Models #Combinatorics #Conditional expectation #Conditional probability distribution #Conditional variance #Covariate #Econometrics #Estimator #FOS: Mathematics #Mathematics #Probability mass function #Random variable #Regular conditional probability #Statistic #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #math.ST #msc:62F12 #msc:62G05 #msc:62J99 #stat.TH
paper · pdf · doi:10.48550/arxiv.1903.10914
published in arXiv (Cornell University) (Cornell University) · 35 pages
arxiv created 2019/03/26 · openalex publication_date 2019/03/26 · arxiv updated 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable X to sums over every k-tuple of distinct observations of X. They may be used to estimate a regular functional θ(PX) of the law of X. When a vector of covariates Z is available, a conditional U-statistic may describe the effect of z on the conditional law of X given Z=z, by estimating a regular conditional functional θ(PX|Z=⋅). We prove concentration inequalities for conditional U-statistics. 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 non-asymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods.