The Annals of Mathematical Statistics

Asymptotically Optimal Tests for Finite Markov Chains

Luis B. Boza

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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.

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

First available in Project Euclid: 27 April 2007

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

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