On general bootstrap of empirical estimator of a semi-Markov kernel with applications

The aim of this paper is to introduce a general bootstrap by exchangeable weight random variables for empirical estimators of the semi-Markov kernels and of the conditional transition probabilities for semi-Markov processes with countable state space. Asymptotic properties of these generalized bootstrapped empirical distributions are obtained by a martingale approach. We show how to apply our results to the construction of confidence intervals and change point problem where the limiting distribution of the proposed statistic is derived under the null hypothesis.