The Automatic Construction of Bootstrap Confidence Intervals

The standard intervals, for example, $\theta ̂\pm 1.96\sigma ̂$ for nominal 95% two-sided coverage, are familiar and easy to use, but can be of dubious accuracy in regular practice. Bootstrap confidence intervals offer an order of magnitude improvement—from first order to second order accuracy. This article introduces a new set of algorithms that automate the construction of bootstrap intervals, substituting computer power for the need to individually program particular applications. The algorithms are described in terms of the underlying theory that motivates them, along with examples of their application. They are implemented in the R package bcaboot. Supplementary materials for this article are available online.