FDR control with pseudo-gatekeeping based on a possibly data driven order of the hypotheses. We propose a multiple testing procedure controlling the false discovery rate. The procedure is based on a possibly data driven ordering of the hypotheses, which are tested at the uncorrected level q until a suitable number is not rejected. When the order is data driven, larger effect sizes are considered first, therefore selecting more interesting hypotheses with larger probability. The proposed procedure is valid under independence for the test statistics. We also propose a modification which makes our procedure valid under arbitrary dependence. It is shown in simulation that we compare particularly well when the sample size is small. We conclude with an application to identification of molecular signatures of intracranial ependymoma. The methods are implemented in an R package (someMTP), freely available on CRAN.

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