ANTITHETIC VARIABLES CONTROL VARIATES Variance Reduction Background the simulation error for some parameter depends on MSE Var Var n so the simulation can be more ecient if Var is reduced

Antithetic Variables Key idea if and are id RVs with mean Var Var Var 2 Cov X so variance is reduced if and have Cov X 0 For many simulations a estimator is U for some so consider the antithetic estimator 1 Combined estimator is 2 Notes a

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