Sparse linear system identification can be performed through convex optimization, by the minimization of an l1-norm functional. If an errors-in-variables model is considered, the problem is more challenging as inherently non-convex. The l1-norm approach for the errors-in-variables model is studied in recent literature. In this work, we propose to replace thel1-norm functional by a concave functional. Concave functionals have been shown to improve the performance in practical experiments of sparse linear regression; nevertheless, theoretical analyses of this improvement are missing in the errors-in-variables setting. The goal of this paper is to fill this gap, by studying conditions that guarantee that the concave approach is variable selection consistent. Moreover, we illustrate how to implement it throughl1reweighting techniques, and we present numerical simulations that show its effectiveness.
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