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math.ST2014★ 28 cited
Information Geometry Approach to Parameter Estimation in Markov Chains
Masahito Hayashi, Shun Watanabe
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…
math.ST2014★ 37 cited
Finite-length Analysis on Tail probability for Markov Chain and Application to Simple Hypothesis Testing
Shun Watanabe, Masahito Hayashi
Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean. Employing these bounds, we obtain upper and lower bounds o…