  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.
