Optimal antithetic sampling plans

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Abstract
Antithetic sampling, a broad family of sampling plans developed by Hammersley and Morton (1956) and Handscomb (1958), is one of the most popular variance reduction techniques being used in simulation. However, many antithetic sampling plans are too computationally complex to be of practical use in simulation. Moreover, the only generally applicable methods for deriving optimal antithetic sampling plans, Hammersley and Handscomb (1964) and Andréasson (1972a, 1972b, 1972c), are very uneconomic in practice since they require that the variance covariance matrix of all likely antithetic estimates be known. Computational considerations which determine the efficiency of any antithetic sampling plan are used to identify systematic sampling plans as an efficient and appropriate subset of the Hammersley and Handscomb family. This subset includes all of the extensions of antithetic sampling in the literature The problem of identifying the least variance antithetic sampling plan for use with a given model sampling algorithm can be formulated as a transportation assignment problem and solved using a branch and bound procedure. The optimization technique developed is applied only in the context of model sampling, that is, the replication of independent, identically distributed random variables. However, one of the examples illustrates that these resuits can be extended to applications in queueing system simulation.

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