Abstract
In this paper we consider the sampling properties of the bootstrap process, that is, the empirical process obtained from a random sample of size n (with replacement) of a fixed sample of size n of a continuous distribution. The cumulants of the bootstrap process are given up to the order n −1 and their unbiased estimation is discussed. Furthermore, it is shown that the bootstrap process has an asymptotic minimax property for some class of distributions up to the order n −1/2.
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Akahira, M., Takeuchi, K. Bootstrap method and empirical process. Ann Inst Stat Math 43, 297–310 (1991). https://doi.org/10.1007/BF00118637
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DOI: https://doi.org/10.1007/BF00118637