- Volume 3, Number 2 (1997), 149-179.
Second-order properties of an extrapolated bootstrap without replacement under weak assumptions
This paper shows that a straightforward extrapolation of the bootstrap distribution obtained by resampling without replacement, as considered by Politis and Romano, leads to second-order correct confidence intervals, provided that the resampling size is chosen adequately. We assume only that the statistic of interest Tn, suitably renormalized by a regular sequence, is asymptotically pivotal and admits an Edgeworth expansion on some differentiable functions. The results are extended to a corrected version of the moving-block bootstrap without replacement introduced by Künsch for strong-mixing random fields. Moreover, we show that the generalized jackknife or the Richardson extrapolation of such bootstrap distributions, as considered by Bickel and Yahav, leads to better approximations.
Bernoulli, Volume 3, Number 2 (1997), 149-179.
First available in Project Euclid: 25 April 2007
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Bertail, Patrice. Second-order properties of an extrapolated bootstrap without replacement under weak assumptions. Bernoulli 3 (1997), no. 2, 149--179. https://projecteuclid.org/euclid.bj/1177526727