Open Access
August 2016 Information geometry approach to parameter estimation in Markov chains
Masahito Hayashi, Shun Watanabe
Ann. Statist. 44(4): 1495-1535 (August 2016). DOI: 10.1214/15-AOS1420


We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.


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Masahito Hayashi. Shun Watanabe. "Information geometry approach to parameter estimation in Markov chains." Ann. Statist. 44 (4) 1495 - 1535, August 2016.


Received: 1 February 2015; Revised: 1 November 2015; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1347.62182
MathSciNet: MR3519931
Digital Object Identifier: 10.1214/15-AOS1420

Primary: 62M05

Keywords: asymptotic efficient estimator , expectation parameter , exponential family , Fisher information matrix , natural parameter , Relative entropy

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
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