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Approximating a sequence of observations by a simple process
Dinah Rosenberg, Eilon Solan, and Nicolas Vieille
Source: Ann. Statist. Volume 32, Number 6
(2004), 2742-2775.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1107794886
Digital Object Identifier: doi:10.1214/009053604000000643
Mathematical Reviews number (MathSciNet): MR2145156
Zentralblatt MATH identifier: 1071.62075
References
Aldous, D. J. and Fill, J. A. (2002). Reversible Markov chains and random walks on graphs. Available at www.stat.berkeley.edu/users/aldous.
Alon, N., Spencer, J. H. and Erdös, P. (2000). The Probabilistic Method, 2nd ed. Wiley, New York.
Mathematical Reviews (MathSciNet): MR1885388
Zentralblatt MATH: 0996.05001
Baum, L. E. and Eagon, J. A. (1967). An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology. Bull. Amer. Math. Soc. 73 360--363.
Mathematical Reviews (MathSciNet): MR210217
Digital Object Identifier: doi:10.1090/S0002-9904-1967-11751-8
Baum, L. E. and Petrie, T. (1966). Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Statist. 37 1554--1563.
Mathematical Reviews (MathSciNet): MR202264
Digital Object Identifier: doi:10.1214/aoms/1177699147
Feller, W. (1968). An Introduction to Probability Theory and Its Applications 1, 3rd ed. Wiley, New York.
Mathematical Reviews (MathSciNet): MR228020
Glynn, P. W. and Ormoneit, D. (2002). Hoeffding's inequality for uniformly ergodic Markov chains. Statist. Probab. Lett. 56 143--146.
Mathematical Reviews (MathSciNet): MR1881167
Jerrum, M. and Sinclair, A. (1989). Approximating the permanent. SIAM J. Comput. 18 1149--1178.
Mathematical Reviews (MathSciNet): MR1025467
Digital Object Identifier: doi:10.1137/0218077
Zentralblatt MATH: 0723.05107
Krogh, A., Mian, I. S. and Haussler, D. (1994). A hidden Markov model that finds genes in E. coli DNA. Nucleic Acids Research 22 4768--4778.
Lovász, L. and Kannan, R. (1999). Faster mixing via average conductance. In Proc. 31st Annual ACM Symposium on Theory of Computing 282--287. ACM, New York.
Mathematical Reviews (MathSciNet): MR1798047
Lovász, L. and Simonovits, M. (1990). The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume. In Proc. 31st Annual Symposium on Foundations of Computer Science 1 346--354. IEEE, Piscataway, NJ.
Mathematical Reviews (MathSciNet): MR1150706
Rabiner, L. R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77 257--286.
Solan, E. and Vieille, N. (2003). Perturbed Markov chains. J. Appl. Probab. 40 107--122.
Mathematical Reviews (MathSciNet): MR1953770
Digital Object Identifier: doi:10.1239/jap/1044476830
Zentralblatt MATH: 1026.60090
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