Unbiased Estimation of The Reciprocal Mean For Non-Negative Random Variables

In recent years, Monte Carlo estimators have been proposed that can estimate the ratio of two expectations without bias. We investigate the theoretical properties of a Taylor-expansion based estimator of the reciprocal mean of a non-negative random variable. We establish explicit expressions for the computational efficiency of this estimator and obtain optimal choices for its parameters. We also derive corresponding practical confidence intervals and show that they are asymptotically equivalent to the maximum likelihood (biased) ratio estimator as the simulation budget increases.