Exchangeably Weighted Bootstraps of General Markov U-Process

Abstract

We explore an exchangeably weighted bootstrap of the general function-indexed empirical U-processes in the Markov setting, which is a natural higher-order generalization of the weighted bootstrap empirical processes. As a result of our findings, a considerable variety of bootstrap resampling strategies arise. This paper aims to provide theoretical justifications for the exchangeably weighted bootstrap consistency in the Markov setup. General structural conditions on the classes of functions (possibly unbounded) and the underlying distributions are required to establish our results. This paper provides the first general theoretical study of the bootstrap of the empirical U-processes in the Markov setting. Potential applications include the symmetry test, Kendall’s tau and the test of independence.