On the accuracy of the bootstrap approximation of the joint distribution of sample quantiles

Abstract

It is proved that the accuracy of the bootstrap approximation of the joint distribution of sample quantiles lies between O(n^−1/4) and O(n^−1/4 a_n), where (log(n))1/2=O(a_n). As an application, we investigated confidence intervals based on the bootstrap.

Keywords:

• Confidence interval
• normal approximation
• Bahadur representation