Robust Parametric Inference for Finite Markov Chains
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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 the minimization of a suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from the underlying first-order stationary Markov chain, we have defined the minimum density power divergence estimator (MDPDE) of the underlying parameter and rigorously derive its asymptotic and robustness properties under appropriate conditions. The performance of our proposed MDPDEs are illustrated theoretically as well as empirically for several common examples of finite Markov chain models. The application of the MDPDE in robust testing of statistical hypotheses is discussed along with the (parametric) comparison of two Markov chain sequences. Finally, several directions for extending the proposed approach of MDPDE and related inference are also briefly discussed for some useful extended set-ups like multiple sequences of Markov chains, higher order Markov chains and non-stationary Markov chains with time-dependent transition probabilities.
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