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Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. (English) Zbl 1089.62502
Summary: Current scientific techniques in genomics and image processing routinely produce hypothesis testing problems with hundreds or thousands of cases to consider simultaneously. This poses new difficulties for the statistician, but also opens new opportunities. In particular, it allows empirical estimation of an appropriate null hypothesis. The empirical null may be considerably more dispersed than the usual theoretical null distribution that would be used for any one case considered separately. An empirical Bayes analysis plan for this situation is developed, using a local version of the false discovery rate to examine the inference issues. Two genomics problems are used as examples to show the importance of correctly choosing the null hypothesis.

MSC:
62C12 Empirical decision procedures; empirical Bayes procedures
62P10 Applications of statistics to biology and medical sciences; meta analysis
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