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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.06323 |
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| _version_ | 1866917292911099904 |
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| author | Perry, Ronan Xu, Zichun McGough, Olivia Witten, Daniela |
| author_facet | Perry, Ronan Xu, Zichun McGough, Olivia Witten, Daniela |
| contents | In recent years, there has been substantial interest in the task of selective inference: inference on a parameter that is selected from the data. Many of the existing proposals fall into what we refer to as the \emph{infer-and-widen} framework: they produce symmetric confidence intervals whose midpoints do not account for selection and therefore are biased; thus, the intervals must be wide enough to account for this bias. In this paper, we investigate infer-and-widen approaches in three vignettes: the winner's curse, maximal contrasts, and inference after the lasso. In each of these examples, we show that a state-of-the-art infer-and-widen proposal leads to confidence intervals that are wider than a non-infer-and-widen alternative. Furthermore, even an ``oracle'' infer-and-widen confidence interval -- the narrowest possible interval that could be theoretically attained via infer-and-widen -- can be wider than the alternative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infer-and-widen, or not? Perry, Ronan Xu, Zichun McGough, Olivia Witten, Daniela Methodology In recent years, there has been substantial interest in the task of selective inference: inference on a parameter that is selected from the data. Many of the existing proposals fall into what we refer to as the \emph{infer-and-widen} framework: they produce symmetric confidence intervals whose midpoints do not account for selection and therefore are biased; thus, the intervals must be wide enough to account for this bias. In this paper, we investigate infer-and-widen approaches in three vignettes: the winner's curse, maximal contrasts, and inference after the lasso. In each of these examples, we show that a state-of-the-art infer-and-widen proposal leads to confidence intervals that are wider than a non-infer-and-widen alternative. Furthermore, even an ``oracle'' infer-and-widen confidence interval -- the narrowest possible interval that could be theoretically attained via infer-and-widen -- can be wider than the alternative. |
| title | Infer-and-widen, or not? |
| topic | Methodology |
| url | https://arxiv.org/abs/2408.06323 |