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December 2004 Approximating a sequence of observations by a simple process
Dinah Rosenberg, Eilon Solan, Nicolas Vieille
Ann. Statist. 32(6): 2742-2775 (December 2004). DOI: 10.1214/009053604000000643


Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence.

We generalize the result to the case where the one-step transitions are required to be in given polyhedra.


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Dinah Rosenberg. Eilon Solan. Nicolas Vieille. "Approximating a sequence of observations by a simple process." Ann. Statist. 32 (6) 2742 - 2775, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1071.62075
MathSciNet: MR2145156
Digital Object Identifier: 10.1214/009053604000000643

Primary: 60J99 , 62M09 , 93E03

Keywords: data approximation , hidden Markov chains , Markov chains , nonhomogenous Markov chains

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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