The Annals of Mathematical Statistics

Asymptotically Optimal Tests for Finite Markov Chains

Luis B. Boza

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Abstract

A discrete time, finite Markov chain with fixed initial state and stationary transition behavior is considered. Using Whittle's formula a large deviation result (similar to Hoeffding's result for one multinomial distribution) is obtained for the transition count matrix of a path of the chain of arbitrary length. This result is then used in the asymptotic comparison of a given sequence of tests about the transition probability matrix with a suitably constructed sequence of likelihood ratio tests. It is assumed that the sizes of these tests decrease to zero at a certain rate as the length of the observed path increases. The comparison is carried out at fixed alternatives in terms of the behavior of the ratio of type-II-error probabilities.

Article information

Source
Ann. Math. Statist., Volume 42, Number 6 (1971), 1992-2007.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177693067

Digital Object Identifier
doi:10.1214/aoms/1177693067

Mathematical Reviews number (MathSciNet)
MR300383

Zentralblatt MATH identifier
0246.62085

JSTOR
links.jstor.org

Citation

Boza, Luis B. Asymptotically Optimal Tests for Finite Markov Chains. Ann. Math. Statist. 42 (1971), no. 6, 1992--2007. doi:10.1214/aoms/1177693067. https://projecteuclid.org/euclid.aoms/1177693067


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