Zerbib, NissimNissimZerbibYen-Huan LiHsieh, Ya-PingYa-PingHsiehCevher, VolkanVolkanCevher2019-05-072019-05-072016https://doi.org/10.1109/ALLERTON.2016.7852263https://scholars.lib.ntu.edu.tw/handle/123456789/406503https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015222060&doi=10.1109%2fALLERTON.2016.7852263&partnerID=40&md5=28147d0e44fcb23e624d9df6953bcc2aMonticello, IL, USAThis paper presents a non-asymptotic upper bound for the estimation error of the constrained lasso, under the high-dimensional (n ≪ p) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be estimated is not exactly sparse (e.g., when it is weakly sparse), and shows explicitly the effect of overestimating the ℓ1-norm of the parameter to be estimated on the estimation performance. The results of this paper show that the constrained lasso is minimax optimal for estimating a parameter with bounded ℓ1-norm, and also for estimating a weakly sparse parameter if its ℓ1-norm is accessible. © 2016 IEEE.Errors; Estimation; Error bound; Estimation errors; Estimation performance; High-dimensional; Minimax; Non-asymptotic; Upper Bound; Parameter estimationconference paper10.1109/ALLERTON.2016.78522632-s2.0-85015222060