Variance Reduction for Bernouilli Response Variables

A method to reduce the sampling errors in simulations performed to estimate the expectation of a dichotomous variable is suggested. It is equivalent to the variance reduction technique known as Control Variates. The new estimator is unbiased. Some ways to estimate its variance (and to estimate the true amount of variance reduction) are suggested. A simulation study (a sort of simulation into a simulation, requiring the use of supercomputing techniques) is presented in order to show the validity of this approach in the determination of the power of a test.