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- Title
Model selection properties of forward selection and sequential cross‐validation for high‐dimensional regression.
- Authors
Wieczorek, Jerzy; Lei, Jing
- Abstract
Forward selection (FS) is a popular variable selection method for linear regression. But theoretical understanding of FS with a diverging number of covariates is still limited. We derive sufficient conditions for FS to attain model selection consistency. Our conditions are similar to those for orthogonal matching pursuit, but are obtained using a different argument. When the true model size is unknown, we derive sufficient conditions for model selection consistency of FS with a data‐driven stopping rule, based on a sequential variant of cross‐validation. As a byproduct of our proofs, we also have a sharp (sufficient and almost necessary) condition for model selection consistency of "wrapper" forward search for linear regression. We illustrate intuition and demonstrate performance of our methods using simulation studies and real datasets.
- Subjects
ORTHOGONAL matching pursuit; WRAPPERS
- Publication
Canadian Journal of Statistics, 2022, Vol 50, Issue 2, p454
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.11635