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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24875 |
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| _version_ | 1866914422761455616 |
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| author | Shen, Qinyan Gregory, Karl Huang, Xianzheng |
| author_facet | Shen, Qinyan Gregory, Karl Huang, Xianzheng |
| contents | We propose a unified framework to draw inferences for regression coefficients in a generalized linear model (GLM) following Lasso-based variable selection. We adapt to non-Gaussian GLMs a recently developed parametric programming strategy for post-selection inference in the linear model with a Gaussian response by drawing parallels between maximum likelihood estimation in GLMs and least squares estimation in linear models. We then conduct post-selection inference based on a linearized model for pseudo response and covariate data strategically created based on the raw data. Using synthetic data generated from regression models for three different types of non-Gaussian responses in simulation experiments, we demonstrate that the proposed method effectively corrects the naive inference that ignores variable selection while achieving greater efficiency than a polyhedral-based post-selection adjustment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Post-selection inference in generalized linear models via parametric programming Shen, Qinyan Gregory, Karl Huang, Xianzheng Methodology We propose a unified framework to draw inferences for regression coefficients in a generalized linear model (GLM) following Lasso-based variable selection. We adapt to non-Gaussian GLMs a recently developed parametric programming strategy for post-selection inference in the linear model with a Gaussian response by drawing parallels between maximum likelihood estimation in GLMs and least squares estimation in linear models. We then conduct post-selection inference based on a linearized model for pseudo response and covariate data strategically created based on the raw data. Using synthetic data generated from regression models for three different types of non-Gaussian responses in simulation experiments, we demonstrate that the proposed method effectively corrects the naive inference that ignores variable selection while achieving greater efficiency than a polyhedral-based post-selection adjustment. |
| title | Post-selection inference in generalized linear models via parametric programming |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.24875 |