On a linear method in bootstrap confidence intervals

Abstract

A linear method for the construction of asymptotic bootstrap confidence intervals is proposed. We approximate asymptotically pivotal and non-pivotal quantities, which are smooth functions of means of n independent and identically distributed random variables, by using a sum of n independent smooth functions of the same analytical form. Errors are of order Op(n-3/2) and Op(n-2), respectively. The linear method allows a straightforward approximation of bootstrap cumulants, by considering the set of n independent smooth functions as an original random sample to be resampled with replacement.