Approximating high-dimensional infinite-order \(U\)-statistics: statistical and computational guarantees

DOI10.1214/19-EJS1643zbMath1434.62071arXiv1901.01163MaRDI QIDQ2283566

Yanglei Song, Xiaohui Chen, Kengo Kato

Publication date: 3 January 2020

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01163

zbMATH Keywords

bootstraprandom forestsGaussian approximationuncertainty quantificationincomplete \(U\) statisticsinfinite-order \(U\)-statistics

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Order statistics; empirical distribution functions (62G30)

Related Items (13)

CLT For U-statistics With Growing Dimension ⋮ Edgeworth expansions for network moments ⋮ Rates of convergence for random forests via generalized U-statistics ⋮ High-dimensional central limit theorems for homogeneous sums ⋮ Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors ⋮ On the variable bandwidth kernel estimation of conditional \(U\)-statistics at optimal rates in sup-norm ⋮ Central limit theorems for high dimensional dependent data ⋮ Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ High-dimensional central limit theorems by Stein's method ⋮ Unnamed Item ⋮ Gaussian approximations for high-dimensional non-degenerate \(U\)-statistics via exchangeable pairs ⋮ Stratified incomplete local simplex tests for curvature of nonparametric multiple regression

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