Strong consistency of the stationary bootstrap under ψ-weak dependence

Abstract

This work deals with the stationary bootstrap of Politis and Romano (1994) for theψ-weakly dependent sequences proposed by Doukhan and Louhichi (1999), establishing strong consistency of the bootstrap sample variance and the bootstrap sample mean under the dependence structure for the observed process. This extends the results of Politis and Romano (1994) and Shao and Yu (1993). © 2011 Elsevier B.V.