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Finding Dantzig selectors with a proximity operator based fixed-point algorithm

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  • Prater, Ashley
  • Shen, Lixin
  • Suter, Bruce W.

Abstract

A simple iterative method for finding the Dantzig selector, designed for linear regression problems, is introduced. The method consists of two stages. The first stage approximates the Dantzig selector through a fixed-point formulation of solutions to the Dantzig selector problem; the second stage constructs a new estimator by regressing data onto the support of the approximated Dantzig selector. The proposed method is compared to an alternating direction method. The results of numerical simulations using both the proposed method and the alternating direction method on synthetic and real-world data sets are presented. The numerical simulations demonstrate that the two methods produce results of similar quality; however the proposed method tends to be significantly faster.

Suggested Citation

  • Prater, Ashley & Shen, Lixin & Suter, Bruce W., 2015. "Finding Dantzig selectors with a proximity operator based fixed-point algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 36-46.
    • Handle: RePEc:eee:csdana:v:90:y:2015:i:c:p:36-46
    DOI: 10.1016/j.csda.2015.04.005
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    References listed on IDEAS

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    3. Robert Tibshirani, 2011. "Regression shrinkage and selection via the lasso: a retrospective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 273-282, June.
    4. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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