Computation of Exact Bootstrap Confidence Intervals: Complexity and Deterministic Algorithms

Abstract

The bootstrap method is one of the major developments in statistics in the 20th century for computing confidence intervals directly from data. However, the bootstrap method is traditionally approximated with a randomized algorithm, which can sometimes produce inaccurate confidence intervals. In “Computation of Exact Bootstrap Confidence Intervals: Complexity and Deterministic Algorithms,” Bertsimas and Sturt present a new perspective of the bootstrap method through the lens of counting integer points in a polyhedron. Through this perspective, the authors develop the first computational complexity results and efficient deterministic approximation algorithm (fully polynomial time approximation scheme) for bootstrap confidence intervals, which unlike traditional methods, has guaranteed bounds on its error. In experiments on real and synthetic data sets from clinical trials, the proposed deterministic algorithms quickly produce reliable confidence intervals, which are significantly more accurate than those from randomization.