Information Geometry Approach to Parameter Estimation in Markov Chains
Statistics Theory
2016-09-28 v4 Information Theory
math.IT
Statistics Theory
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.
Cite
@article{arxiv.1401.3814,
title = {Information Geometry Approach to Parameter Estimation in Markov Chains},
author = {Masahito Hayashi and Shun Watanabe},
journal= {arXiv preprint arXiv:1401.3814},
year = {2016}
}
Comments
Appendix D is added