Hall, Peter On the number of bootstrap simulations required to construct a confidence interval. (English) Zbl 0611.62048 Ann. Stat. 14, 1453-1462 (1986). Suppose we obtain one-sided confidence intervals for a parameter \(\theta\) by ”smooth” Studentized statistic using B bootstrap simulations. It is shown that the reduction of error of coverage probability from \(O(n^{- 1/2})\) to \(O(n^{-1})\) is available uniformly in B provided nominal coverage probability is a multiple of \((B+1)^{-1}\). This improvement is possible even when B is fixed and n is allowed to increase. Further it is shown that for large n, the simulated statistic values behave like random observations from a continuous distribution unless B increases faster than any power of n. The effect of discrete nature of the bootstrap statistic is felt only if B increases exponentially with n. Reviewer: B.K.Kale Cited in 1 ReviewCited in 42 Documents MSC: 62G15 Nonparametric tolerance and confidence regions 62E20 Asymptotic distribution theory in statistics 65C99 Probabilistic methods, stochastic differential equations Keywords:Edgeworth inversion; number of simulations; one-sided confidence intervals; Studentized statistic; bootstrap simulations; reduction of error; coverage probability Citations:Zbl 0611.62047 PDFBibTeX XMLCite \textit{P. Hall}, Ann. Stat. 14, 1453--1462 (1986; Zbl 0611.62048) Full Text: DOI