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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 42, Fasc. 2,
pages 283 - 302
DOI: 10.37190/0208-4147.00066
Published online 25.11.2022
 

Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal

T. Skalski
P. Graczyk
B. Kołodziejek
M. Wilczyński

Abstract:

Sorted l1 Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows the reduction of the model dimension by shrinking some estimates of the regression coefficients completely to zero or by equating the absolute values of some nonzero estimates of these coefficients. This allows one to identify situations where some of true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on the strong consistency of pattern recovery by SLOPE when the design matrix is orthogonal and illustrate advantages of the SLOPE clustering in the context of high frequency signal denoising.

2010 AMS Mathematics Subject Classification: Primary 62J05; Secondary 62J07.

Keywords and phrases: linear regression, SLOPE, signal denoising.

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