Bootstrapping the sample means for stationary mixing sequences (Q1313135)

To make the bootstrap suitable for dependent observations many authors [among them \textit{H. R. Künsch}, Ann. Stat. 17, No. 3, 1217-1241 (1989; Zbl 0684.62035)] have introduced various block resampling procedures. In this paper a circular block resampling procedure, modifying Künsch's procedure, is proposed. This 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. Two general theorems on bootstrapping sample means for stationary sequences are proved. Applications to stationary \(\alpha\)-mixing, \(\rho\)- mixing and \(\varphi\)-mixing sequences are also discussed.