Antithetic Variates Revisited.

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 covariance structures induced by the techniques separately and together are derived and conditions under which they are optimal sampling plans are described. Rates of convergence for the variance of the sample mean are given for bounded, continuous and discrete random variables and for unbounded continuous random variables with special, although commonly encountered, structure. Author