Approximating a sequence of observations by a simple process

Dinah Rosenberg (1) , Nicolas Vieille (2) , Eilon Solan (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
3 TAU - Tel Aviv University

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.

Mots clés: Markov chains; data approximation; nonhomogenous Markov chains; hidden Markov chains

Domaines: Economie et sciences de la décision

Dinah Rosenberg, Nicolas Vieille, Eilon Solan. Approximating a sequence of observations by a simple process. Annals of Statistics, 2004, Vol.32,n°6, pp.2742-2775. ⟨10.1214/009053604000000643⟩. ⟨hal-00464946⟩