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The Dantzig selector for high dimensional statistical problems

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The Dantzig selector has been introduced by Emmanuel Candés and Terence Tao in an outstanding paper that deals with prediction and variable selection in the setting of the curse of dimensionality extensively considered in statistics recently. Using sparsity assumptions, variable selection performed by the Dantzig selector can improve estimation accuracy by effectively identifying the subset of important predictors, and then enhance model interpretability allowed by parsimonious representations. The goal of this talk is to present the main ideas of the paper by Candés and Tao and the remarkable results they obtained. We also wish to emphasize some of the extensions proposed in different settings and in particular for density estimation considered in the dictionary approach. Finally, connections between the Dantzig selector and the popular lasso procedure will be also highlighted.

This talk is part of the LMS Invited Lectures 2011 series.

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