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 $\theta(\hat{F})$.