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Abstract:
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Benjamini and Yekutieli (2005) introduced the concept of false coverage rate (FCR) for simultaneous confidence intervals which is parallel to the concept of FDR. We consider the FCR criterion to be too stringent, requiring that it is controlled (in the frequentist's sense) for all the possible unknown parameter values. This is especially true if the number of unknown parameters is large, for example tens of thousands as in modern applications like microarray. We propose and study a less stringent criterion, the control of the empirical Bayes FCR for confidence intervals, which, by some analytic and numerical calculations, were demonstrated to have the FCR controlled at level q for a class of prior distributions. Furthermore, the proposed empirical Bayes intervals are always shorter than in average length (and could be one third as long as) the intervals of Benjamini and Yekutieli (2005).
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