Approximating a sequence of observations by a simple process

Dinah Rosenberg*, Eilon Solan, Nicolas Vieille

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2742-2775
Number of pages34
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 2004


  • Data approximation
  • Hidden Markov chains
  • Markov chains
  • Nonhomogenous Markov chains


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