Post-selection inference of generalized linear models based on the lasso and the elastic net

Abstract

Post-selection inference has been an active research topic recently. A lot of work provided different ways to solve practical problems in many fields such as medicine, finance, and so on. In particular, post-selection inference under the linear model is widely discussed. We extend it to generalized linear model and present new approaches for post-selection inference for penalized least squares method. The core of this framework is the distribution function of the post-selection estimation conditioned on the selection event. Then, lasso and elastic net are used to select models to construct the effective confidence interval of the selected coefficient. The theoretical results and the numerical comparisons show that our methods are better than the existing ones. Finally, the proposed methods are applied to the analysis of real data sets.

Keywords:

• Post-selection inference
• generalized linear models
• confidence interval
• lasso
• elastic net

Additional information

Funding

This paper is supported by NNSF projects of China (11701318, 11871294), NSF project of Shandong Province of China (ZR2019PF012, ZR2019BA028), and a project of Shandong Province higher educational science and technology program (J18KA356).