Information geometry approach to parameter estimation in Markov chains
Masahito Hayashi, Shun Watanabe
The Annals of Statistics · 2016 · Volume 44 · Issue 4
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.
Keywords
62M05, asymptotic efficient estimator, expectation parameter, exponential family, Fisher information matrix, natural parameter, Relative entropy
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