论文标题
有限马尔可夫链的强大参数推断
Robust Parametric Inference for Finite Markov Chains
论文作者
论文摘要
我们考虑了参数有限的马尔可夫链模型中统计推断的问题，并通过最小化了流行密度功率差异的合适（经验）版本来开发定义过渡概率的参数的强大估计器。基于一阶固定马尔可夫链的一系列观测，我们定义了基础参数的最小密度差异估计量（MDPDE），并严格得出了其在适当条件下其渐近和鲁棒性的。在理论上和经验上说明了MDPDES的性能，并在经验上说明了有限的马尔可夫链模型的一些常见示例。还讨论了其在统计假设的可靠测试中的应用以及两个马尔可夫链序列的（参数）比较。还针对马尔可夫链，高阶马尔可夫链和非平稳的马尔可夫链的多个序列简要讨论了扩展MDPDE和相关推理的几个方向，并具有时间依赖性的过渡概率。最后，我们的建议用于分析三个国际市场的公司信用评级移民数据。
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.
