Second-order correctness of the blockwise bootstrap for stationary observations

Abstract

We show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second-order correct provided we choose an appropriate variance estimator. We also show how to adapt the $BC_a$ confidence interval of Efron to the a dependent case. For the proofs we extend the results of Götze and Hipp on the validity of the formal Edgeworth expansion for a sum to the studentized mean.