🤖 AI Summary
This work proposes a unified inference framework based on parametric programming to address the bias in statistical inference for regression coefficients following Lasso variable selection in generalized linear models. By locally linearizing the maximum likelihood estimator, the method constructs a linear relationship between pseudo-responses and covariates, thereby extending parametric programming—previously limited to Gaussian settings—to non-Gaussian response distributions. This extension enables valid post-selection inference across a range of exponential family models, including logistic and Poisson regression. The approach maintains computational efficiency while substantially improving inferential accuracy. Simulation studies demonstrate that, in non-Gaussian settings, the proposed method effectively corrects the naive inference that ignores the selection process and achieves higher statistical efficiency compared to existing approaches such as the polyhedral method.
📝 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.