An analysis of the SPARSEVA estimate for the finite sample data case. (October 2018)

• Record Type: Journal Article
• Authors: Ha, Huong; Welsh, James S.; Rojas, Cristian R.; Wahlberg, Bo
• Is Part Of: Automatica. Volume 96(2018)
• Page Start: 141
• Page End: 149
• Publication Date: 2018-10
• Subjects: SPARSEVA estimate -- Estimation error -- Upper bound -- Finite sample data; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.06.046
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional l 1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.