The law of large numbers for \(U\)-statistics under absolute regularity

DOI10.1214/ECP.v3-988zbMath0901.60015MaRDI QIDQ1389782

Miguel A. Arcones

Publication date: 5 July 1998

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/119624

zbMATH Keywords

law of large numbers\(U\)-statisticsabsolute regularitybeta-mixing conditionstrictly stationary sequence of random variables

Mathematics Subject Classification ID

Strong limit theorems (60F15)

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Multivariate Autoregressive Time Series Using Schweppe Weighted Wilcoxon Estimates ⋮ Asymptotic behaviour of the empirical distance covariance for dependent data ⋮ Efficient Estimation of an Additive Quantile Regression Model ⋮ Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences ⋮ Limit theorems for U-statistics of Bernoulli data ⋮ Marcinkiewicz–Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators ⋮ Some remarks on MCMC estimation of spectra of integral operators ⋮ Some remarks on the ergodic theorem for \(U\)-statistics ⋮ A simple variance inequality for \(U\)-statistics of a Markov chain with applications ⋮ The weak convergence for self-normalized \(U\)-statistics with dependent samples ⋮ Qualitative robustness of von Mises statistics based on strongly mixing data ⋮ A Quantile Regression Model for Time-Series Data in the Presence of Additive Components ⋮ Marcinkiewicz-Zygmund strong laws for \(U\)-statistics of weakly dependent observations ⋮ EMPIRICAL LIKELIHOOD CONFIDENCE INTERVALS FOR DEPENDENT DURATION DATA ⋮ A Projection-Based Nonparametric Test of Conditional Quantile Independence

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