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Robust parametric inference for finite Markov chains
TEST ( IF 1.3 ) Pub Date : 2021-04-26 , DOI: 10.1007/s11749-021-00771-1
Abhik Ghosh

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.



中文翻译:

有限马尔可夫链的鲁棒参数推断

我们考虑参数有限马尔可夫链模型中的统计推断问题,并通过最小化流行密度幂散度的合适(经验)版本,开发出定义过渡概率的参数的鲁棒估计器。基于对一阶平稳马尔可夫链的一连串观察,我们定义了基础参数的最小密度幂散估计(MDPDE),并在适当的条件下严格推导了其渐近性和鲁棒性。对于有限Markov链模型的一些常见示例,从理论上和经验上都说明了MDPDE的性能。还讨论了它在统计假设的稳健测试中的应用以及两个马尔可夫链序列的(参数)比较。对于具有时间相关转移概率的马尔可夫链,高阶马尔可夫链和非平稳马尔可夫链的多个序列,还简要讨论了扩展MDPDE和相关推论的几个方向。最后,我们的建议被应用于分析三个国际市场的企业信用评级迁移数据。

更新日期:2021-04-27
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