The almost sure invariance principles of degenerate \(U\)-statistics of degree two for stationary random variables

DOI10.1016/0304-4149(94)90141-4zbMath0805.60026OpenAlexW2078123819MaRDI QIDQ1316605

Ken-ichi Yoshihara, Shuya Kanagawa

Publication date: 29 January 1995

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(94)90141-4

zbMATH Keywords

\(U\)-statisticsalmost sure invariance principlechi-square processesphi-mixing processesHilbert-Schmidt expansion

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (2)

Nuclearity of a nonnegative definite integral kernel on a separable metric space ⋮ Asymptotic Behavior of Optimal Weighting in Generalized Self‐Normalization for Time Series

Cites Work

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• The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals
• Invariance principles for von Mises and U-statistics
• Estimates of Characteristic Functions of Some Random Variables with Applications to $\omega ^2 $-Statistics. II
• Limit theorems for sums of weakly dependent Banach space valued random variables
• Almost sure invariance principles for partial sums of weakly dependent random variables
• A Non-Parametric Test of Independence

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