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April 2017 Finite-length analysis on tail probability for Markov chain and application to simple hypothesis testing
Shun Watanabe, Masahito Hayashi
Ann. Appl. Probab. 27(2): 811-845 (April 2017). DOI: 10.1214/16-AAP1216

Abstract

Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean for the Markov chain with finite state space. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the type-2 error under the exponential constraint for the error probability of the type-1 error in a simple hypothesis testing for a finite-length Markov chain, which yields the Hoeffding-type bound. For these derivations, we derive upper and lower bounds of cumulant generating function for Markov chain with finite state space. As a byproduct, we obtain another simple proof of central limit theorem for Markov chain with finite state space.

Citation

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Shun Watanabe. Masahito Hayashi. "Finite-length analysis on tail probability for Markov chain and application to simple hypothesis testing." Ann. Appl. Probab. 27 (2) 811 - 845, April 2017. https://doi.org/10.1214/16-AAP1216

Information

Received: 1 May 2015; Revised: 1 May 2016; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1368.62235
MathSciNet: MR3655854
Digital Object Identifier: 10.1214/16-AAP1216

Subjects:
Primary: 62F03, 62M02

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 2017
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