Derivative estimation with known control-variate variances

We investigate the conception that the sample variance of the control variate (CV) should be used for estimating the optimal linear CV weight, even when the CV variance is known. A mixed estimator, which uses an estimate of the correlation of the performance measure (Y) and the control (X) is evaluated. Results indicate that the mixed estimator has most potential benefit when no information on the correlation of X and Y is available, especially when sample sizes are small. This work is presented in terms of CV for familiarity, but its primary application is in derivative estimation. In this context, unlike CV, X and Y are not assumed to be correlated.