Bootstrapping the sample means for stationary mixing sequences

Abstract

We propose a circular block resampling procedure to modify Künsch's moving block bootstrap. Our procedure has the special feature that the resampled data are like drawing from the empirical distribution function of dependent observations. No information is lost concerning the nature of dependency of the original observations coming from a general stationary sequence. We prove two general theorems on bootstrapping sample means for stationary sequences. Applications to stationary α-mixing, ρ-mixing and φ-mixing sequences are also discussed.