Fast confidence bounds for the false discovery proportion over a path of hypotheses
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917323228577792 |
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| author | Durand, Guillermo |
| author_facet | Durand, Guillermo |
| contents | This paper presents a new algorithm (and an additional trick) that allows to compute fastly an entire curve of post hoc bounds for the False Discovery Proportion when the underlying bound $V^*\_{\mathfrak{R}}$ construction is based on a reference family $\mathfrak{R}$ with a forest structure {à} la Durand et al. (2020). By an entire curve, we mean the values $V^*\_{\mathfrak{R}}(S\_1),\dotsc,V^*\_{\mathfrak{R}}(S\_m)$ computed on a path of increasing selection sets $S\_1\subsetneq\dotsb\subsetneq S\_m$, $|S\_t|=t$. The new algorithm leverages the fact that going from $S\_t$ to $S\_{t+1}$ is done by adding only one hypothesis. Compared to a more naive approach, the new algorithm has a complexity in $O(|\mathcal K|m)$ instead of $O(|\mathcal K|m^2)$, where $|\mathcal K|$ is the cardinality of the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast confidence bounds for the false discovery proportion over a path of hypotheses Durand, Guillermo Statistics Theory Computation Methodology This paper presents a new algorithm (and an additional trick) that allows to compute fastly an entire curve of post hoc bounds for the False Discovery Proportion when the underlying bound $V^*\_{\mathfrak{R}}$ construction is based on a reference family $\mathfrak{R}$ with a forest structure {à} la Durand et al. (2020). By an entire curve, we mean the values $V^*\_{\mathfrak{R}}(S\_1),\dotsc,V^*\_{\mathfrak{R}}(S\_m)$ computed on a path of increasing selection sets $S\_1\subsetneq\dotsb\subsetneq S\_m$, $|S\_t|=t$. The new algorithm leverages the fact that going from $S\_t$ to $S\_{t+1}$ is done by adding only one hypothesis. Compared to a more naive approach, the new algorithm has a complexity in $O(|\mathcal K|m)$ instead of $O(|\mathcal K|m^2)$, where $|\mathcal K|$ is the cardinality of the family. |
| title | Fast confidence bounds for the false discovery proportion over a path of hypotheses |
| topic | Statistics Theory Computation Methodology |
| url | https://arxiv.org/abs/2502.03849 |