Simultaneous confidence intervals uniformly more likely to determine signs

Yoav Benjamini, Vered Madar and Philip B. Stark

Biometrika, 2013, vol. 100, issue 2, 283-300

Abstract: Many studies draw inferences about multiple endpoints but ignore the statistical implications of multiplicity. Effects inferred to be positive when there is no adjustment for multiplicity can lose their statistical significance when multiplicity is taken into account, perhaps explaining why such adjustments are so often omitted. We develop new simultaneous confidence intervals that mitigate this problem; these are uniformly more likely to determine signs than are standard simultaneous confidence intervals. When one or more of the parameter estimates are small, the new intervals sacrifice some length to avoid crossing zero; but when all the parameter estimates are large, the new intervals coincide with standard simultaneous confidence intervals, so there is no loss of precision. When only a small fraction of the estimates are small, the procedure can determine signs essentially as well as one-sided tests with prespecified directions, incurring only a modest penalty in maximum length. The intervals are constructed by inverting level-α tests to form a 1 - α confidence set, and then projecting that set onto the coordinate axes to get confidence intervals. The tests have hyper-rectangular acceptance regions that minimize the maximum amount by which the acceptance region protrudes from the orthant that contains the hypothesized parameter value, subject to a constraint on the maximum side-length of the hyper-rectangle. Copyright 2013, Oxford University Press.

Date: 2013
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