Approximating a sequence of observations by a simple process

Details Approximating a sequence of observations by a simple process Approximating a sequence of observations by a simple process

2005-08-30

arxiv.org/abs/math/0508607v1

Annals of Statistics 2004, Vol. 32, No. 6, 2742-2775

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000643 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000643

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.

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