Simulation-Based Estimation of Proportions

Simulated estimates for several proportions are needed in many simulation studies. We propose a method for controlling the length of a simulation run so that the proportions estimated satisfy a prespecified precision requirement.

The method applies the arcsin transform in order to generate confidence intervals with the desired width. The Bonferroni inequality is applied in a new way to construct a rectangular confidence area for the proportions being estimated. Since we are using the Bonferroni inequality, we can use the existing methods developed for estimating the variance of a single mean.

The properties of the method proposed depend on three factors: 1) the arcsin transform, 2) the proposed way of applying the Bonferroni inequality, and 3) the method for estimating the variance. We examine the effects that the transform and the way of applying the Bonferroni inequality have.

Empirical results indicate that the method provides estimates that satisfy the prespecified precision requirement, when the spectral method is used to estimate the variances of the proportions. In addition, simulation runs, when estimating either several proportions or the corresponding mean, are about the same lengths.