Markov Chains and Their Extensions

  • M. B. Rajarshi
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


This chapter deals with likelihood-based inference for ergodic finite as well as infinite Markov chains. We also consider extensions of Markov chain models, such as Hidden Markov chain, Markov chains based on polytomous regression, and Raftery’s Mixture Transition Density model. These models have less number of parameters as compared to a higher order finite Markov chain. Lastly, we discuss methods of estimation in grouped data from finite Markov chains.


Markov Chain Markov Chain Model Fisher Information Matrix Finite Markov Chain Hide Markov Chain 
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  1. Adke, S.R., Deshmukh, S.R.: Limit distribution of a higher order Markov chains. J. Roy. Stat. Soc. Ser. B 50, 105–108 (1988)Google Scholar
  2. Berchtold, A., Raftery, A.E.: Mixture transition distribution model for high-order markov chains and non-gaussian time series. Stat. Sci. 17, 328–356 (2002)Google Scholar
  3. Billingsley, P.: Statistical Inference for Markov Processes. The University of Chicago Press, Chicago (1961)Google Scholar
  4. Cappé, O., Moulines, E., Ryden, T.: Inference in Hidden Markov Models. Springer, New York (2005)Google Scholar
  5. Davison, A.C.: Statistical Models. Cambridge University Press, Cambridge (2003)Google Scholar
  6. Elliot, R.J., Aggaoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control. Springer, New York (1995)Google Scholar
  7. Guttorp, P.: Stochastic Modeling of Scientific Data. Chapman and Hall, London (1995)Google Scholar
  8. Inderdeep Kaur, Rajarshi: Ridge regression for estimation of transition probabilities from aggregate data. Commun. Stat. Simul. Comput. 41, 524–530 (2012)Google Scholar
  9. Katz, R.W.: On some criteria for estimating the order of a markov chain. Technometrics 23, 243–249 (1981)Google Scholar
  10. Lee, T.C., Judge, G.G., Zellner, A.: Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data. North Holland, Amsterdam (1970)Google Scholar
  11. Lindsey, J.K.: Statistical Analysis of Stochastic Processes in Time. Cambridge University Press, Cambridge (2004)Google Scholar
  12. MacDonald, I., Zucchini. W.: Hidden Markov and Other Models for Discrete-Valued Time Series. Chapman and Hall, London (1997)Google Scholar
  13. Manning, C.D., Schütze, H.: Statistical Natural Language Processing. MIT Press, Cambridge (1999)Google Scholar
  14. Raftery, A.E.: A model for high order Markov chains. J. Roy. Stat. Soc. Ser. B 47, 528–539 (1985)Google Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of PunePuneIndia

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