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2017 Quantile universal threshold
Caroline Giacobino, Sylvain Sardy, Jairo Diaz-Rodriguez, Nick Hengartner
Electron. J. Statist. 11(2): 4701-4722 (2017). DOI: 10.1214/17-EJS1366


Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to zero, estimators such as lasso, elastic net and subset selection perform variable selection. One crucial step challenges all these estimators: the amount of thresholding governed by a threshold parameter $\lambda $. If too large, important features are missing; if too small, incorrect features are included. Within a unified framework, we propose a selection of $\lambda $ at the detection edge. To that aim, we introduce the concept of a zero-thresholding function and a null-thresholding statistic, that we explicitly derive for a large class of estimators. The new approach has the great advantage of transforming the selection of $\lambda $ from an unknown scale to a probabilistic scale. Numerical results show the effectiveness of our approach in terms of model selection and prediction.


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Caroline Giacobino. Sylvain Sardy. Jairo Diaz-Rodriguez. Nick Hengartner. "Quantile universal threshold." Electron. J. Statist. 11 (2) 4701 - 4722, 2017.


Received: 1 March 2017; Published: 2017
First available in Project Euclid: 24 November 2017

zbMATH: 1384.62258
MathSciNet: MR3729656
Digital Object Identifier: 10.1214/17-EJS1366

Keywords: Convex optimization , high-dimensionality , regularization , Sparsity , thresholding


Vol.11 • No. 2 • 2017
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