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Acta Mathematica Vietnamica

RATE OF CONVERGENCE IN BOOTSTRAP APPROXIMATIONS WITH RANDOM SAMPLE SIZE

icon-email NGUYEN VAN TOAN

Abstract

We give the convergence rates of the random sample size bootstrap approximations of the distribution of the sample mean. Using the quantity αn2=E[(Nnn1)2], where Nn is the random sample size, we obtain a convergence rate O(n12(loglogn)12) if αn=O(n12(loglogn)12).