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

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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.