A nonparametric coherent confidence procedure

Holm's step-down testing procedure starts with the smallest p-value and sequentially screens larger p-values without any information on confidence intervals. This article changes the conventional step-down testing framework by presenting a nonparametric procedure that starts with the largest p-value and sequentially screens smaller p-values in a step-by-step manner to construct a set of simultaneous confidence sets. We use a partitioning approach to prove that the new procedure controls the simultaneous confidence level (thus strongly controlling the familywise error rate). Discernible features of the new stepwise procedure include consistency with individual inference, coherence, and confidence estimations for follow-up investigations. In a simple simulation study, the proposed procedure (treated as a testing procedure), is more powerful than Holm's procedure when the correlation coefficient is large, and vice versa when it is small. In the data analysis of a medical study, the new procedure is able to detect the efficacy of Aspirin as a cardiovascular prophylaxis in a nonparametric setting.