Limit distributions of conditional \(U\)-statistics

DOI10.1007/BF02212880zbMath0819.60034OpenAlexW2463808992MaRDI QIDQ1890737

Arusharka Sen, B. L. S. Prakasa Rao

Publication date: 23 May 1995

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02212880

zbMATH Keywords

multiple Wiener integrallimit distributionsconditional \(U\)-statistics

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic distribution theory in statistics (62E20) Limit theorems in probability theory (60F99)

Related Items

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 ⋮ 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 ⋮ Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional \(U\)-statistics involving functional data ⋮ Asymptotic distribution of the Kaplan-Meier \(U\)-statistics.

Cites Work

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• Symmetric statistics, Poisson point processes, and multiple Wiener integrals
• Asymptotic distribution of symmetric statistics
• Conditional \(U\)-statistics
• Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points