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October 1996 Second-order correctness of the blockwise bootstrap for stationary observations
F. Götze, H. R. Künsch
Ann. Statist. 24(5): 1914-1933 (October 1996). DOI: 10.1214/aos/1069362303


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.


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F. Götze. H. R. Künsch. "Second-order correctness of the blockwise bootstrap for stationary observations." Ann. Statist. 24 (5) 1914 - 1933, October 1996.


Published: October 1996
First available in Project Euclid: 20 November 2003

zbMATH: 0906.62040
MathSciNet: MR1421154
Digital Object Identifier: 10.1214/aos/1069362303

Primary: 62M10
Secondary: 62E20 , 62G15

Keywords: $BC_a$ confidence interval , dependent data , Edgeworth expansion , Resampling , Strong mixing , studentization , time series

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 5 • October 1996
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