## The Annals of Statistics

### 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.

#### Article information

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

Dates
First available in Project Euclid: 20 November 2003

https://projecteuclid.org/euclid.aos/1069362303

Digital Object Identifier
doi:10.1214/aos/1069362303

Mathematical Reviews number (MathSciNet)
MR1421154

Zentralblatt MATH identifier
0906.62040

#### 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