Deriving the asymptotic distribution of \(U\)- and \(V\)-statistics of dependent data using weighted empirical processes

DOI10.3150/11-BEJ358zbMath1452.62190arXiv1207.5899OpenAlexW2054221867MaRDI QIDQ442076

Eric Beutner, Henryk Zähle

Publication date: 9 August 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.5899

zbMATH Keywords

weighted empirical processJordan decompositionweak dependencefunctional delta methodquasi-Hadamard differentiabilitystationary sequence of random variablesU- and V-statistic

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

Related Items (20)

Two-sample U-statistic processes for long-range dependent data ⋮ Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals ⋮ Limit theorems for U-statistics of Bernoulli data ⋮ Functional weak limit theorem for a local empirical process of non-stationary time series and its application ⋮ Kaplan-Meier V- and U-statistics ⋮ On estimation of limiting variance of partial sums of functions of associated random variables ⋮ Exponential inequalities for dependent V-statistics via random Fourier features ⋮ Approximating class approach for empirical processes of dependent sequences indexed by functions ⋮ On limiting distribution of U-statistics based on associated random variables ⋮ Rank-based change-point analysis for long-range dependent time series ⋮ Qualitative robustness of von Mises statistics based on strongly mixing data ⋮ A general approach to the joint asymptotic analysis of statistics from sub-samples ⋮ Continuous mapping approach to the asymptotics of \(U\)- and \(V\)-statistics ⋮ Inference of weighted \(V\)-statistics for nonstationary time series and its applications ⋮ Limit theorems for nondegenerate \(U\)-statistics of continuous semimartingales ⋮ New measure of the bivariate asymmetry ⋮ An Extended Continuous Mapping Theorem for Outer Almost Sure Weak Convergence ⋮ Dependent Wild Bootstrap for the Empirical Process ⋮ Weak convergence of the weighted sequential empirical process of some long-range dependent data ⋮ Donsker results for the empirical process indexed by functions of locally bounded variation and applications to the smoothed empirical process

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