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      Quantile universal threshold: model selection at the detection edge for high-dimensional linear regression

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          Abstract

          To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify with high probability part of the significant covariates asymptotically, and are numerically tractable thanks to convexity. Yet, the selection of a threshold parameter \(\lambda\) remains crucial in practice. To that aim we propose Quantile Universal Thresholding, a selection of \(\lambda\) at the detection edge. We show with extensive simulations and real data that an excellent compromise between high true positive rate and low false discovery rate is achieved, leading also to good predictive risk.

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          Author and article information

          Journal
          05 December 2014
          Article
          1412.1927
          67b22a76-e8ba-4d4d-b0bf-87547e82f649

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          stat.ML stat.ME

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