Antithetic randomization with correlation -1/(K-1) is necessary and sufficient to keep the randomization variance of cross-validation bounded in the small-bias limit, and the jointly normal antithetic scheme is minimax optimal within a general class.
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On the optimality of antithetic randomization for cross-validation
Antithetic randomization with correlation -1/(K-1) is necessary and sufficient to keep the randomization variance of cross-validation bounded in the small-bias limit, and the jointly normal antithetic scheme is minimax optimal within a general class.