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Degrees of freedom in lasso problems
Open accessAbstract
We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix $X$. Like the well-known result of Zou, Hastie and Tibshirani [Ann. Statist. 35 (2007) 2173–2192], which gives the degrees of freedom of the lasso fit when $X$ has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitrary predictor matrix $X$ (and an arbitrary penalty matrix $D$). Though our focus is degrees of freedom, we establish some intermediate results on the lasso and generalized lasso that may be interesting on their own.
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Cited by
A significance test for the lasso
Lockhart, R., Taylor, J., Tibshirani, R. J., & Tibshirani, R. (2014) · The Annals of Statistics · doi:10.1214/13-aos1175 · Cited by 541
Self-citationThe lasso problem and uniqueness
Tibshirani, R. J. (2013) · Electronic Journal of Statistics · doi:10.1214/13-ejs815 · Cited by 507
Self-citationLassopack: model selection and prediction with regularized regression in Stata
Ahrens, A., Hansen, C. B., & Schaffer, M. E. (2020) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x20909697 · Cited by 212
Chen, W., McDonnell, S. K., Thibodeau, S. N., Tillmans, L. S., & Schaid, D. J. (2016) · Genetics · doi:10.1534/genetics.116.188953 · Cited by 52
Metadata
- Authors
- Tibshirani, R. J., & Taylor, J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2012-04-01
- Volume
- 40
- Issue
- 2
- Pages
- 1198-1232
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1974563846
- Cited by
- 239
- References
- 0
- FWCI
- 9.29
- Type
- journal article
- Language
- en
- Open access
- green
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