2014/01/01 by Alexandre Belloni, Belloni, Alexandre, Mathieu Rosenbaum +4 · 65 citations
Engineering · Mathematics · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Computation (stat.CO) #Computer science #Conic section #Control Systems and Identification #Estimator #FOS: Computer and information sciences #FOS: Mathematics #Lasso (programming language) #Linear model #Linear programming #Linear regression #Mathematical optimization #Mathematics #Minimax #Minimax estimator #Minimum-variance unbiased estimator #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #math.ST #stat.CO #stat.TH
paper · pdf · doi:10.48550/arxiv.1408.0241
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2014/01/01 · arxiv created 2016/07/03 · arxiv updated 2016/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider the linear regression model with observation error in the design.\nIn this setting, we allow the number of covariates to be much larger than the\nsample size. Several new estimation methods have been recently introduced for\nthis model. Indeed, the standard Lasso estimator or Dantzig selector turn out\nto become unreliable when only noisy regressors are available, which is quite\ncommon in practice. We show in this work that under suitable sparsity\nassumptions, the procedure introduced in Rosenbaum and Tsybakov (2013) is\nalmost optimal in a minimax sense and, despite non-convexities, can be\nefficiently computed by a single linear programming problem. Furthermore, we\nprovide an estimator attaining the minimax efficiency bound. This estimator is\nwritten as a second order cone programming minimisation problem which can be\nsolved numerically in polynomial time.\n