Information Geometry Approach to Parameter Estimation in Markov Chains

Abstract

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.

Appendix D is added

References in corpus (3)

• Maximum Likelihood Estimation for Markov Chains
• The exponential family of Markov chains and its information geometry
• Parallel Distributed Block Coordinate Descent Methods based on Pairwise Comparison Oracle

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