Robust parametric inference for finite Markov chains

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