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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| _version_ | 1797076115821428736 |
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| author | Meinshausen, N Rice, J |
| author_facet | Meinshausen, N Rice, J |
| author_sort | Meinshausen, N |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:59:35Z |
| format | Journal article |
| id | oxford-uuid:757526f3-44dd-4f6a-9ea9-d2a715efffaf |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:59:35Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:757526f3-44dd-4f6a-9ea9-d2a715efffaf2022-03-26T20:09:27ZEstimating the proportion of false null hypotheses among a large number of independently tested hypothesesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:757526f3-44dd-4f6a-9ea9-d2a715efffafSymplectic Elements at Oxford2006Meinshausen, NRice, JWe 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. |
| spellingShingle | Meinshausen, N Rice, J Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses |
| title | Estimating the proportion of false null hypotheses among a large number
of independently tested hypotheses |
| title_full | Estimating the proportion of false null hypotheses among a large number
of independently tested hypotheses |
| title_fullStr | Estimating the proportion of false null hypotheses among a large number
of independently tested hypotheses |
| title_full_unstemmed | Estimating the proportion of false null hypotheses among a large number
of independently tested hypotheses |
| title_short | Estimating the proportion of false null hypotheses among a large number
of independently tested hypotheses |
| title_sort | estimating the proportion of false null hypotheses among a large number of independently tested hypotheses |
| work_keys_str_mv | AT meinshausenn estimatingtheproportionoffalsenullhypothesesamongalargenumberofindependentlytestedhypotheses AT ricej estimatingtheproportionoffalsenullhypothesesamongalargenumberofindependentlytestedhypotheses |