Information geometry approach to parameter estimation in Markov chains

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.

• Publication year

  2014

• Venue

  2014 IEEE International Symposium on Information Theory

• Publication date

  2014-01-16

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1214/15-AOS1420arXiv 1401.3814
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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