For exchangeable hypotheses the optimal FWER-controlling multiple-testing procedure is computed via elementary symmetric polynomials on likelihood ratios plus a monotonicity theorem that enables an efficient bisection coordinate-descent algorithm.
Edgar Dobriban, Kristen Fortney, Stuart K
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Optimal multiple testing under family-wise error control: elementary symmetric polynomials and a scalable algorithm
For exchangeable hypotheses the optimal FWER-controlling multiple-testing procedure is computed via elementary symmetric polynomials on likelihood ratios plus a monotonicity theorem that enables an efficient bisection coordinate-descent algorithm.