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arXiv · 2603.24875

Post-selection inference in generalized linear models via parametric programming

Qinyan Shen·Karl Gregory·Xianzheng Huang
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Abstract

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.

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Qinyan Shen, Karl Gregory, Xianzheng Huang. 2026-03-25. Post-selection inference in generalized linear models via parametric programming. https://doi.org/10.5705/ss.202025.0194

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