A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913342105321472 |
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| author | Kostic, Anica Fryzlewicz, Piotr |
| author_facet | Kostic, Anica Fryzlewicz, Piotr |
| contents | For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $λ$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $λ$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing Kostic, Anica Fryzlewicz, Piotr Methodology For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $λ$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $λ$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data. |
| title | A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing |
| topic | Methodology |
| url | https://arxiv.org/abs/2309.10017 |