The Annals of Statistics

Second-order correctness of the blockwise bootstrap for stationary observations

F. Götze and H. R. Künsch

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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.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 1914-1933.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362303

Digital Object Identifier
doi:10.1214/aos/1069362303

Mathematical Reviews number (MathSciNet)
MR1421154

Zentralblatt MATH identifier
0906.62040

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G15: Tolerance and confidence regions 62E20: Asymptotic distribution theory

Keywords
Resampling Edgeworth expansion studentization $BC_a$ confidence interval time series dependent data strong mixing

Citation

Götze, F.; Künsch, H. R. Second-order correctness of the blockwise bootstrap for stationary observations. Ann. Statist. 24 (1996), no. 5, 1914--1933. doi:10.1214/aos/1069362303. https://projecteuclid.org/euclid.aos/1069362303


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