Some notes on ergodic theorem for \(U\)-statistics of order \(m\) for stationary and not necessarily ergodic sequences

DOI10.1016/J.SPL.2024.110117zbMATH Open1541.60021MaRDI QIDQ6569450

Davide Giraudo

Publication date: 9 July 2024

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

ergodic theorem\(U\)-statisticsstationary sequences

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Cites Work

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• Distance covariance in metric spaces
• Limit theorems for von Mises statistics of a measure preserving transformation
• Marcinkiewicz-Zygmund strong laws for \(U\)-statistics of weakly dependent observations
• The law of large numbers for \(U\)-statistics under absolute regularity
• Strong laws for 𝐿- and 𝑢-statistics
• Limit theorems for U-statistics of Bernoulli data
• A Class of Statistics with Asymptotically Normal Distribution
• U-Statistics in Stochastic Geometry
• Some remarks on the ergodic theorem for \(U\)-statistics

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