Utilizing a Quantile Function Approach to Obtain Exact Bootstrap Solutions

Abstract

The popularity of the bootstrap is due in part to its wide applicability and the ease of implementing resampling procedures on modern computers. But careful reading of Efron (1979) will show that at its heart, the bootstrap is a "plug-in'' procedure that involves calculating a functional $\theta(\hat{F})$ from an estimate of the c.d.f. F. Resampling becomes invaluable when, as is often the case, $\theta(\hat{F})$ cannot be calculated explicitly. We discuss some situations where working with the sample quantile function, $\hat{Q}$, rather than $\hat{F}$, can lead to explicit (exact) solutions to $\theta(\hat{F})$.