Mathematical Sciences: Statistical Inference for Markov Chains and Regression Models: Estimation, Bootstrapping and Related Asymptotics

被称为“bootstrap”的统计推断重采样方法在数据来自独立同分布随机变量的观测值的情况下被证明是有用的，本研究将把该方法扩展到马尔可夫链中遇到的一种简单的依赖。我们要考虑的一种情况是具有可数状态空间和齐次转移概率的马尔可夫链。是否有可能提供经验转移概率和真实转移概率之差分布的自举描述的问题将进行研究。研究具有有限、可数和不可数状态空间的循环马尔可夫链的命中时间分布、平稳分布等估计的相关问题。

The method of resampling for statistical inference known as the "bootstrap" has proved useful in situations where the data are observations from independent identically distributed random variables and this research will extend the method to a simple kind of dependence encountered in the Markov chain. One case that will be considered is that of a Markov chain with a countable state space and homogeneous transition probabilities. The question of whether or not it is possible to provide bootstrap descriptions of the distribution of the difference of the empirical and true transition probabilities will be examined. Related questions for the estimation of the distribution of hitting times, stationary distributions, etc., for recurrent Markov chains with finite, countable and uncountable state spaces will be studied.