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We introduce two new variance estimation procedures that use non-overlapping and overlapping blocks, respectively. The non-overlapping blocks estimator can be viewed as the limit of the thinned block bootstrap estimator recently proposed in Guan Loh (2007), by letting the number of thinned processes and bootstrap samples therein both increase to infinity. The non-overlapping blocks estimator can be obtained quickly since it does not require any thinning or bootstrap steps, and it is more stable. The overlapping blocks estimator further improves the performance of the non-overlapping blocks with a modest increase in computation time. A simulation study demonstrates the superiority of the proposed estimators over the thinned block bootstrap estimator.