Antithetic Variates Revisited

Abstract

This paper extends earlier results in the area of variance reduction techniques applied to simulation on a computer. In particular, it views the antithetic sampling technique as a combination of rotation and reflection sampling on a circle. The correlation structures induced by the techniques separately and together are derived and conditions under which they are optimal sampling plans are described. We also introduce the concept of the average correlation coefficient as an equivalent way of assessing the effect of rotation and reflection sampling. A randomized assignment procedure is described for making this average correlation exact between every pair of the n random variables. © 1983, ACM. All rights reserved.