Invariance principles for U-statistics and von Mises functionals

DOI10.1016/0378-3758(89)90099-2zbMath0674.62016OpenAlexW1987366529MaRDI QIDQ1121612

Beate Babbel

Publication date: 1989

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(89)90099-2

zbMATH Keywords

weak invariance principlecovariance structuremoment conditionsabsolutely regularKiefer processesdegenerate U-statisticsuniformly mixingnew type of stochastic integral

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Stationary stochastic processes (60G10) Stochastic integrals (60H05) Functional limit theorems; invariance principles (60F17)

Related Items (8)

Invariance Principles for Products ofU-Statistics Without Variance ⋮ The strong law of \(U\)-statistics with \(\varphi\)-mixing samples ⋮ Dependent wild bootstrap for degenerate \(U\)- and \(V\)-statistics ⋮ Degenerate \(U\)- and \(V\)-statistics under ergodicity: asymptotics, bootstrap and applications in statistics ⋮ Degenerate \(U\)- and \(V\)-statistics under weak dependence: asymptotic theory and bootstrap consistency ⋮ The weak convergence for self-normalized \(U\)-statistics with dependent samples ⋮ Change-Point Detection Under Dependence Based on Two-Sample U-Statistics ⋮ Limit theorems for von Mises statistics of a measure preserving transformation

Cites Work

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• A note on invariance principles for v. Mises' statistics
• On the \(\varphi\)-mixing condition for stationary random sequences
• Functional limit theorems for U-statistics in the degenerate case
• Note on multidimensional empirical processes for \(\Phi\)-mixing random vectors
• Weak convergence of generalized U-statistics
• On U-statistics and v. mise? statistics for weakly dependent processes
• Almost sure approximation theorems for the multivariate empirical process
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• An almost sure invariance principle for the empirical distribution function of mixing random variables
• Invariance principles for dependent variables
• An intrinsic time for non-stationary finite markov chains
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
• Mises’ Theorem on the Asymptotic Behavior of Functionals of Empirical Distribution Functions and Its Statistical Applications
• A Class of Statistics with Asymptotically Normal Distribution
• On the Asymptotic Distribution of Differentiable Statistical Functions
• Consistency and Unbiasedness of Certain Nonparametric Tests

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