We consider post-selection inference for high-dimensional (generalized) linear models. Data carving from Fithian, Sun and Taylor  is a promising technique to perform this task. However, it suffers from the instability of the model selector and hence, may lead to poor replicability, especially in high-dimensional settings. We propose the multicarve method inspired by multisplitting to improve upon stability and replicability. Furthermore, we extend existing concepts to group inference and illustrate the applicability of the methodology also for generalized linear models.
The research of C. Schultheiss and P. Bühlmann was supported in part by the European Research Council under the Grant Agreement No 786461 (CausalStats – ERC-2017-ADG).
"Multicarving for high-dimensional post-selection inference." Electron. J. Statist. 15 (1) 1695 - 1742, 2021. https://doi.org/10.1214/21-EJS1825