Conditional \(U\)-statistics

DOI10.1214/aop/1176990452zbMath0770.60035OpenAlexW1991181610MaRDI QIDQ1176155

Winfried Stute

Publication date: 25 June 1992

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176990452

zbMATH Keywords

strong convergencesmoothingasymptotic normalityweak and strong consistencyconditional \(U\)-statistics

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Linear inference, regression (62J99) Strong limit theorems (60F15)

Related Items (21)

An Application ofU-Statistics to Nonparametric Functional Data Analysis ⋮ Limit distributions of conditional \(U\)-statistics ⋮ Nonparametric confidence bands construction for GLM models with length biased data ⋮ On kernel-based estimation of conditional Kendall's tau: finite-distance bounds and asymptotic behavior ⋮ Optimal choice of the smoothing parameter of conditional \(U\)-statistics ⋮ Ranking and empirical minimization of \(U\)-statistics ⋮ Almost sure representations of weightedU-statistics with applications ⋮ Uniform in bandwidth consistency of conditional \(U\)-statistics adaptive to intrinsic dimension in presence of censored data ⋮ On the variable bandwidth kernel estimation of conditional \(U\)-statistics at optimal rates in sup-norm ⋮ Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data ⋮ Weak-convergence of empirical conditional processes and conditional \(U\)-processes involving functional mixing data ⋮ A class of asymptotically normal degenerate quasi \(U\)-statistics ⋮ Some asymptotic properties of kernel regression estimators of the mode for stationary and ergodic continuous time processes ⋮ Uniform in bandwidth consistency of conditional \(U\)-statistics ⋮ Testing homoscedasticity in nonparametric regression ⋮ Analysis of kernel density estimation of functions of random variables ⋮ Central limit theorems for conditional empirical and conditional \(U\)-processes of stationary mixing sequences ⋮ On the uniform-in-bandwidth consistency of the general conditionalU-statistics based on the copula representation ⋮ Universally consistent conditional \(U\)-statistic for absolutely regular processes and its applications for hidden Markov models ⋮ Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional \(U\)-statistics involving functional data ⋮ Characterization of diagonal symmetry: location unknown, and a test based on allied U-processes

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