The $L$-test: Increasing the Linear Model $F$-test's Power Under Sparsity Without Sacrificing Validity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914174094802944 |
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| author | Paulson, Danielle Sengupta, Souhardya Janson, Lucas |
| author_facet | Paulson, Danielle Sengupta, Souhardya Janson, Lucas |
| contents | We introduce a new procedure for testing the significance of a set of regression coefficients in a Gaussian linear model with $n \geq d$. Our method, the $L$-test, provides the same statistical validity guarantee as the classical $F$-test, while attaining higher power when the nuisance coefficients are sparse. Although the $L$-test requires Monte Carlo sampling, each sample's runtime is dominated by simple matrix-vector multiplications so that the overall test remains computationally efficient. Furthermore, we provide a Monte-Carlo-free variant that can be used for particularly large-scale multiple testing applications. We give intuition for the power of our approach, validate its advantages through extensive simulations, and illustrate its practical utility in both single- and multiple-testing contexts with an application to an HIV drug resistance dataset. In the concluding remarks, we also discuss how our methodology can be applied to a more general class of parametric models that admit asymptotically Gaussian estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L$-test: Increasing the Linear Model $F$-test's Power Under Sparsity Without Sacrificing Validity Paulson, Danielle Sengupta, Souhardya Janson, Lucas Methodology We introduce a new procedure for testing the significance of a set of regression coefficients in a Gaussian linear model with $n \geq d$. Our method, the $L$-test, provides the same statistical validity guarantee as the classical $F$-test, while attaining higher power when the nuisance coefficients are sparse. Although the $L$-test requires Monte Carlo sampling, each sample's runtime is dominated by simple matrix-vector multiplications so that the overall test remains computationally efficient. Furthermore, we provide a Monte-Carlo-free variant that can be used for particularly large-scale multiple testing applications. We give intuition for the power of our approach, validate its advantages through extensive simulations, and illustrate its practical utility in both single- and multiple-testing contexts with an application to an HIV drug resistance dataset. In the concluding remarks, we also discuss how our methodology can be applied to a more general class of parametric models that admit asymptotically Gaussian estimators. |
| title | The $L$-test: Increasing the Linear Model $F$-test's Power Under Sparsity Without Sacrificing Validity |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.23466 |