Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909992730230784 |
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| author | Zhang, Tianyu Lee, Hao Lei, Jing |
| author_facet | Zhang, Tianyu Lee, Hao Lei, Jing |
| contents | We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically normal test statistic, even in high-dimensional settings and with potentially many ties in the population mean vector, by integrating concepts and tools from cross-validation and differential privacy. The key technical ingredient is a central limit theorem for globally dependent data. We also propose practical ways to select the tuning parameter that adapts to the signal landscape. Numerical experiments and data examples demonstrate the ability of the proposed method to achieve a favorable bias-variance trade-off in practical scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection Zhang, Tianyu Lee, Hao Lei, Jing Statistics Theory Methodology Machine Learning We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically normal test statistic, even in high-dimensional settings and with potentially many ties in the population mean vector, by integrating concepts and tools from cross-validation and differential privacy. The key technical ingredient is a central limit theorem for globally dependent data. We also propose practical ways to select the tuning parameter that adapts to the signal landscape. Numerical experiments and data examples demonstrate the ability of the proposed method to achieve a favorable bias-variance trade-off in practical scenarios. |
| title | Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection |
| topic | Statistics Theory Methodology Machine Learning |
| url | https://arxiv.org/abs/2408.02060 |