In this paper, we study the weak convergence to an appropriate Gaussian process of the empirical process of the block-based bootstrap estimator proposed by Künsch for stationary sequences. The classes of processes investigated are weak dependent and associated sequences. We also prove that, differently from the independent situation, the bootstrapped estimator of the mean of certain dependent sequences satisfies the central limit theorem while the mean of the original sequence does not.
"On the blockwise bootstrap for empirical processes for stationary sequences." Ann. Probab. 26 (2) 877 - 901, April 1998. https://doi.org/10.1214/aop/1022855654