2014/01/31 by Masahito Hayashi, Shun Watanabe
Mathematics · Computer Science · #math.ST #cs.IT #math.IT #stat.TH
paper · pdf · doi:10.1214/15-aos1420
published as Annals of Statistics, Volume 44, Number 4, 1495-1535 (2016) · Appendix D is added
arxiv created 2015/05/05 · arxiv updated 2016/09/28
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.