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.
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We generalize the result to the case where the one-step transitions are required to be in given polyhedra.
Publié le : 2004-12-14
Classification:
Markov chains,
data approximation,
nonhomogenous Markov chains,
hidden Markov chains,
60J99,
62M09,
93E03
@article{1107794886,
author = {Rosenberg, Dinah and Solan, Eilon and Vieille, Nicolas},
title = {Approximating a sequence of observations by a simple process},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 2742-2775},
language = {en},
url = {http://dml.mathdoc.fr/item/1107794886}
}
Rosenberg, Dinah; Solan, Eilon; Vieille, Nicolas. Approximating a sequence of observations by a simple process. Ann. Statist., Tome 32 (2004) no. 1, pp. 2742-2775. http://gdmltest.u-ga.fr/item/1107794886/