Double-bootstrap methods that use a single double-bootstrap simulation

TL;DR

This paper introduces a single double-bootstrap sampling technique that achieves third-order accuracy for bias correction with less computational cost, but it does not extend to confidence interval construction.

Contribution

It demonstrates that using a single double-bootstrap sample per bootstrap sample can improve bias correction efficiency and accuracy.

Findings

Single double-bootstrap methods achieve third-order accuracy for bias correction.

These methods require less computational effort than traditional double-bootstrap techniques.

The approach does not improve confidence interval or distribution estimator accuracy.

Abstract

We show that, when the double bootstrap is used to improve performance of bootstrap methods for bias correction, techniques based on using a single double-bootstrap sample for each single-bootstrap sample can be particularly effective. In particular, they produce third-order accuracy for much less computational expense than is required by conventional double-bootstrap methods. However, this improved level of performance is not available for the single double-bootstrap methods that have been suggested to construct confidence intervals or distribution estimators.