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Square-root lasso: Pivotal recovery of sparse signals via conic programming

Publication ,  Journal Article
Belloni, A; Chernozhukov, V; Wang, L
Published in: Biometrika
December 1, 2011

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ nor does it need to pre-estimate σ. Moreover, the method does not rely on normality or sub-Gaussianity of noise. It achieves near-oracle performance, attaining the convergence rate σ(s/n) log p 1/2 in the prediction norm, and thus matching the performance of the lasso with known σ. These performance results are valid for both Gaussian and non-Gaussian errors, under some mild moment restrictions. We formulate the square-root lasso as a solution to a convex conic programming problem, which allows us to implement the estimator using efficient algorithmic methods, such as interior-point and first-order methods. © 2011 Biometrika Trust.

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Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

December 1, 2011

Volume

98

Issue

4

Start / End Page

791 / 806

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

Citation

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Belloni, A., Chernozhukov, V., & Wang, L. (2011). Square-root lasso: Pivotal recovery of sparse signals via conic programming. Biometrika, 98(4), 791–806. https://doi.org/10.1093/biomet/asr043
Belloni, A., V. Chernozhukov, and L. Wang. “Square-root lasso: Pivotal recovery of sparse signals via conic programming.” Biometrika 98, no. 4 (December 1, 2011): 791–806. https://doi.org/10.1093/biomet/asr043.
Belloni A, Chernozhukov V, Wang L. Square-root lasso: Pivotal recovery of sparse signals via conic programming. Biometrika. 2011 Dec 1;98(4):791–806.
Belloni, A., et al. “Square-root lasso: Pivotal recovery of sparse signals via conic programming.” Biometrika, vol. 98, no. 4, Dec. 2011, pp. 791–806. Scopus, doi:10.1093/biomet/asr043.
Belloni A, Chernozhukov V, Wang L. Square-root lasso: Pivotal recovery of sparse signals via conic programming. Biometrika. 2011 Dec 1;98(4):791–806.
Journal cover image

Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

December 1, 2011

Volume

98

Issue

4

Start / End Page

791 / 806

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics