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October 1999 Second-order correctness of the Poisson bootstrap
G. Jogesh Babu, P. K. Pathak, C. R. Rao
Ann. Statist. 27(5): 1666-1683 (October 1999). DOI: 10.1214/aos/1017939146


Rao, Pathak and Koltchinskii have recently studied a sequential approach to resampling in which resampling is carried out sequentially one-by-one (with replacement each time) until the bootstrap sample contains $m \approx (1 - e^{-1})n \approx 0.632n$ distinct observations from the original sample. In our previous work, we have established that the main empirical characteristics of the sequential bootstrap go through, in the sense of being within a distance $O(n^{-3/4})$ from those of the usual bootstrap. However, the theoretical justification of the second-order correctness of the sequential bootstrap is somewhat difficult. It is the main topic of this investigation. Among other things, we accomplish it by approximating our sequential scheme by a resampling scheme based on the Poisson distribution with mean $\mu = 1$ and censored at $X = 0$.


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G. Jogesh Babu. P. K. Pathak. C. R. Rao. "Second-order correctness of the Poisson bootstrap." Ann. Statist. 27 (5) 1666 - 1683, October 1999.


Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0965.62037
MathSciNet: MR2001C:62059
Digital Object Identifier: 10.1214/aos/1017939146

Primary: 62G09
Secondary: 60F05

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 5 • October 1999
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