Bootstrap method and empirical process |
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| Authors: | Masafumi Akahira Kei Takeuchi |
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| Institution: | (1) Institute of Mathematics, University of Tsukuba, 305 Tsukuba, Ibaraki, Japan;(2) Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, 156 Tokyo, Japan |
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| 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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| Keywords: | Bootstrap process cumulants unbiased estimators asymptotic minimax property |
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