Bootstrap confidence intervals for ratios of expectations

ABSTRACT

We are concerned with computing a confidence interval for the ratio E[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.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing

General Terms:
Algorithms

Keywords:
bootstrap, confidence intervals, ratio estimation problem, regenerative simulation