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 a_n² = E[(N_n / n  - 1)²], where N_n  is the random sample size, we obtain a convergence rate O(n^1/2 (loglog n)^1/2)  if  a_n = O(n- 1/2(loglog n)^1/ 2).