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Robust parametric inference for finite Markov chains


We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from a first-order stationary Markov chain, we have defined the minimum density power divergence estimator (MDPDE) of the underlying parameter and rigorously derived its asymptotic and robustness properties under appropriate conditions. Performance of the MDPDEs is illustrated theoretically as well as empirically for some common examples of finite Markov chain models. Its applications in robust testing of statistical hypotheses are also discussed along with (parametric) comparison of two Markov chain sequences. Several directions for extending the MDPDE and related inference are also briefly discussed for multiple sequences of Markov chains, higher order Markov chains and non-stationary Markov chains with time-dependent transition probabilities. Finally, our proposal is applied to analyze corporate credit rating migration data of three international markets.

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The author wishes to thank the editor, the associate editor and two anonymous referees for their careful reading of the manuscript and several constructive suggestions to improve the paper. This research is partially supported by the INSPIRE Faculty Research Grant from Department of Science and Technology, Government of India.

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Correspondence to Abhik Ghosh.

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Ghosh, A. Robust parametric inference for finite Markov chains. TEST 31, 118–147 (2022).

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  • Minimum density power divergence estimator
  • Finite Markov chain
  • Parametric inference
  • Robustness

Mathematics Subject Classification

  • Primary 62F35
  • 62M02
  • Secondary 60J20