Simple expressions of the LASSO and SLOPE estimators in low-dimension. Issue 2 (3rd March 2020)

• Record Type: Journal Article
• Authors: Tardivel, Patrick J. C.; Servien, Rémi; Concordet, Didier
• Is Part Of: Statistics. Volume 54:Issue 2(2020)
• Page Start: 340
• Page End: 352
• Publication Date: 2020-03-03
• Subjects: Best linear unbiased estimator -- LASSO -- SLOPE; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1720019
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : We study the LASSO and SLOPE estimators when the design X satisfies ker ⁡ ( X ) = 0 . Similarly to the LASSO, the SLOPE estimator has an explicit expression when the design matrix X is orthogonal which is reported in the main theorem of this article. We state that, even if the design is not orthogonal, even if residuals are correlated, up to a transformation, the LASSO and SLOPE estimators have a simple expression based on the Best Linear Unbiased Estimator (BLUE). Comparisons with the LASSO estimator show the benefits of the soft-thresholded BLUE.