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Approximating a Sequence of Observations by a Simple Process

Author

Listed:
  • Dinah Rosenberg

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Approximating a Sequence of Observations by a Simple Process," Working Papers hal-00593643, HAL.
    • Handle: RePEc:hal:wpaper:hal-00593643
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    Cited by:

    1. is not listed on IDEAS
    2. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.

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    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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