A simple variance inequality for \(U\)-statistics of a Markov chain with applications

DOI10.1016/j.spl.2012.02.001zbMath1310.60025arXiv1107.2576OpenAlexW1966095645MaRDI QIDQ426715

Pierre Vandekerkhove, Eric Moulines, Gersende Fort, Pierre Priouret

Publication date: 11 June 2012

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

Full work available at URL: https://arxiv.org/abs/1107.2576

zbMATH Keywords

inequalitiesMarkov chainslaw of large numbersU-statisticslimit theorems

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Nonparametric inference (62G99)

Related Items (3)

Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains ⋮ Renewal type bootstrap for increasing degree \(U\)-process of a Markov chain ⋮ A central limit theorem for adaptive and interacting Markov chains

Cites Work

• Markov chains and stochastic stability
• Weak invariance of generalized U-statistics for nonstationary absolutely regular processes
• Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes
• General state space Markov chains and MCMC algorithms
• The law of large numbers for \(U\)-statistics under absolute regularity
• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• Renewal theory and computable convergence rates for geometrically erdgodic Markov chains
• Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
• Limit Theorems for Dependent U-statistics
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