Bootstraps of Martingale‐difference Arrays Under the Uniformly Integrable Entropy
Résumé
This chapter considers the uniform central limit theorem for a bootstrapped martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. It provides some necessary background and states the functional central limit theorem, where the notation and definitions are consistent with the work of Bae et al. The chapter proves the consistency of the bootstrap by establishing the consistency of bootstrapping under general conditions in the framework of martingale-difference arrays. It applies the results of the proof for the bootstrap of the non-parametric semi-Markov kernel estimator.