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December, 1971 Asymptotically Optimal Tests for Finite Markov Chains
Luis B. Boza
Ann. Math. Statist. 42(6): 1992-2007 (December, 1971). DOI: 10.1214/aoms/1177693067


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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Luis B. Boza. "Asymptotically Optimal Tests for Finite Markov Chains." Ann. Math. Statist. 42 (6) 1992 - 2007, December, 1971.


Published: December, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0246.62085
MathSciNet: MR300383
Digital Object Identifier: 10.1214/aoms/1177693067

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 6 • December, 1971
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