Approximating a Sequence of Observations by a Simple Process

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

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 TAU - School of Mathematical Sciences [Tel Aviv]

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.

Keywords: Approximation sequence; Simple process; Statistical method; Probability distribution; Polyhedron

Domains: Economy and decision science

Dinah Rosenberg, Eilon Solan, Nicolas Vieille. Approximating a Sequence of Observations by a Simple Process. 2002. ⟨hal-00593643⟩