An FDR upper bound for an adaptive one-way GBH procedure under exchangeability
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There has been some numerical evidence on the conservativeness of an adaptive one-way GBH procedure for multiple testing the means of equally correlated normal random variables. However, a theoretical investigation into this seems to be lacking. We provide an analytic, non-asymptotic FDR upper bound for such a procedure under the aforementioned multiple testing scenario. The bound is not tight but reasonably quantifies how bad the FDR of the procedure can be. As by-products, we extend two relevant existing results to the setting of p-values that are not necessarily super-uniform.
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