Resumen de Bootstrap Approximation to Distributions of Finite Population U-statistics

Mindaugas Bloznelis

• 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.