Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower $100(1-\alpha)%$ con...
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| Format: | Journal article |
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2006
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| Summary: | We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower $100(1-\alpha)%$ confidence bounds for this proportion, based on the empirical distribution of the $p$-values of the tests. Methods in this family are then compared in terms of ability to consistently estimate the proportion by letting $\alpha \to 0$ as the number of hypothesis tests increases and the proportion decreases. This work is motivated by a signal detection problem that occurs in astronomy. |
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