Functional central limit theorem and Marcinkiewicz strong law of large numbers for Hilbert-valued \(U\)-statistics of absolutely regular data

Central limit and other weak theorems (60F05) Nonparametric statistical resampling methods (62G09) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

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Degenerate \(U\)- and \(V\)-statistics under weak dependence: asymptotic theory and bootstrap consistency
A simple variance inequality for \(U\)-statistics of a Markov chain with applications
Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics
Marcinkiewicz-Zygmund strong laws for \(U\)-statistics of weakly dependent observations
Central limit theorem and the bootstrap for \(U\)-statistics of strongly mixing data
Consistency of the Takens estimator for the correlation dimension
The law of large numbers for \(U\)-statistics under absolute regularity
Optimum bounds for the distributions of martingales in Banach spaces
Asymptotic theory of weakly dependent stochastic processes
Tests for high-dimensional data based on means, spatial signs and spatial ranks
An association test for functional data based on Kendall's tau
Robust inference for change points in high dimension
The conditional central limit theorem in Hilbert spaces.
Limit theorems for functionals of mixing processes with applications to \(U\)-statistics and dimension estimation
Bootstrap forU-statistics: a new approach
Marcinkiewicz–Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators
Limiting behavior of U-statistics for stationary, absolutely regular processes
Strong laws for 𝐿- and 𝑢-statistics
Limit theorems for U-statistics of Bernoulli data
A Wilcoxon-Mann-Whitney-type test for infinite-dimensional data
A Class of Statistics with Asymptotically Normal Distribution
The Theory of Unbiased Estimation
A two sample test based on U-statistic for functional data
Some remarks on the ergodic theorem for \(U\)-statistics

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