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January, 1994 Rates of Convergence for Empirical Processes of Stationary Mixing Sequences
Bin Yu
Ann. Probab. 22(1): 94-116 (January, 1994). DOI: 10.1214/aop/1176988849

Abstract

Classical empirical process theory for Vapnik-Cervonenkis classes deals mainly with sequences of independent variables. This paper extends the theory to stationary sequences of dependent variables. It establishes rates of convergence for $\beta$-mixing and $\phi$-mixing empirical processes indexed by classes of functions. The method of proof depends on a coupling of the dependent sequence with sequences of independent blocks, to which the classical theory can be applied. A uniform $O(n^{-s/(1+s)})$ rate of convergence over V-C classes is established for sequences whose mixing coefficients decay slightly faster than $O(n^{-s})$.

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Bin Yu. "Rates of Convergence for Empirical Processes of Stationary Mixing Sequences." Ann. Probab. 22 (1) 94 - 116, January, 1994. https://doi.org/10.1214/aop/1176988849

Information

Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0802.60024
MathSciNet: MR1258867
Digital Object Identifier: 10.1214/aop/1176988849

Subjects:
Primary: 60F05
Secondary: 60F17 , 60G10

Keywords: $\beta$-mixing , blocking , empirical process , random metric entropy , rate of convergence , V-C class

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • January, 1994
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