Approximating a sequence of observations by a simple process

Dinah Rosenberg, Eilon Solan, Nicolas Vieille

The Annals of Statistics · 2004 · Volume 32 · Issue 6

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.

Keywords

60J99, 62M09, 93E03, data approximation, hidden Markov chains, Markov chains, nonhomogenous Markov chains

Enable JavaScript for citation tools and additional paper interactions.