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Bootstrap Approximation to Distributions of Finite Population U-statistics

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Abstract

We show that the without replacement bootstrap of Booth, Butler and Hall (J. Am. Stat. Assoc. 89, 1282–1289, 1994) provides second order correct approximation to the distribution function of a Studentized U-statistic based on simple random sample drawn without replacement. In order to achieve similar approximation accuracy for the bootstrap procedure due to Bickel and Freedman (Ann. Stat. 12, 470–482, 1984) and Chao and Lo (Sankhya Ser. A 47, 399–405, 1985) we introduce randomized adjustments to the resampling fraction.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius, Lithuania

    Mindaugas Bloznelis

  2. Vilnius University, Naugarduko 24, Vilnius, 03225, Lithuania

    Mindaugas Bloznelis

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  1. Mindaugas Bloznelis
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Correspondence to Mindaugas Bloznelis.

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Bloznelis, M. Bootstrap Approximation to Distributions of Finite Population U-statistics. Acta Appl Math 96, 71–86 (2007). https://doi.org/10.1007/s10440-007-9092-3

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  • DOI: https://doi.org/10.1007/s10440-007-9092-3

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