Simple expressions of the LASSO and SLOPE estimators in low-dimension
Résumé
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.
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