Universally consistent conditional \(U\)-statistic for absolutely regular processes and its applications for hidden Markov models

DOI10.1007/BF02506491zbMath1078.62049MaRDI QIDQ2581129

Michel Harel, Madan Lal Puri

Publication date: 13 January 2006

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

absolute regularity

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Bayesian problems; characterization of Bayes procedures (62C10) Strong limit theorems (60F15)

Cites Work

• Some mixing properties of time series models
• Distribution-free consistency results in nonparametric discrimination and regression function estimation
• Consistent window estimation in nonparametric regression
• Conditional \(U\)-statistics
• Consistent nonparametric regression. Discussion
• Universally consistent conditional \(U\)-statistics
• \(L^ p\)-convergence of conditional \(U\)-statistics
• Conditional \(U\)-statistics for dependent random variables
• Estimation of a multivariate density
• Probability Inequalities for the Sum of Independent Random Variables
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• Statistical Inference for Probabilistic Functions of Finite State Markov Chains

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