Universally consistent conditional \(U\)-statistics

DOI10.1214/aos/1176325378zbMath0818.62049OpenAlexW1970211457MaRDI QIDQ1327852

Winfried Stute

Publication date: 2 July 1995

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

Full work available at URL: https://doi.org/10.1214/aos/1176325378

zbMATH Keywords

nearest neighbor weightsnonparametric discriminationconditional \(U\)- statisticsnearest neighbor estimatorssufficient conditions for universal consistencywindow weights

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Nonparametric estimation (62G05)

Related Items (9)

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 ⋮ Weak-convergence of empirical conditional processes and conditional \(U\)-processes involving functional mixing data ⋮ Model checks for regression: an innovation process approach ⋮ Analysis of kernel density estimation of functions of random variables ⋮ 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

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