Information geometry approach to parameter estimation in Markov chains
M Hayashi, S Watanabe - 2014 IEEE International Symposium …, 2014 - ieeexplore.ieee.org
2014 IEEE International Symposium on Information Theory, 2014•ieeexplore.ieee.org
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.
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.
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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