Exact Post-selection Inference for Forward Stepwise and Least Angle Regression
Year: 2014
Type: preprint
Abstract: In this paper we propose new inference tools for forward stepwise and least angle regression. We first present a general scheme to perform valid inference after any selection event that can be characterized as the observation vector y falling into some polyhedral set. This framework then allows us to derive conditional (post-selection) hypothesis tests at any step of the forward stepwise and least angle regression procedures. We derive an exact null distribution for our proposed test statistics in finite samples, yielding p-values with exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. Application of this framework to general likelihood-based regression models (e.g., generalized linear models and the Cox model) is also discussed.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W172338866