Bootstrap confidence intervals for ratios of expectations

We are concerned with computing a confidence interval for the ratioE[Y]/E[X, where (X,Y) is a pair of random variables. This ratio estimation problem arises in, for instance, regenerative simulation. As an alternative to confidence intervals based on asymptotic normality, we study and compare different variants of the bootstrap for one-sided and two-sided intervals. We point out situations where these techniques provide confidence intervals with coverage much closer to the nominal value than do the classical methods.