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The Square-Root Lasso

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2159)

Abstract

This chapter presents sharp oracle inequalities for the square-root Lasso, applying essentially the same arguments as in Chap. 2 The main new element is that one needs to make sure that the square-root Lasso does not degenerate. After having dealt with this issue, the chapter continues with a comparison of the square-root Lasso with the scaled Lasso. Furthermore, a multivariate version of the square-root Lasso is introduced. The latter will be invoked in later chapters.

Keywords

  • Nuclear Norm
  • Fixed Design
  • Multivariate Version
  • Asymptotic Unbiasedness
  • Asymptotic Lower Bound

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    In this subsection \(\hat{\varSigma }\) is not the Gram matrix X T Xn.

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© 2016 Springer International Publishing Switzerland

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van de Geer, S. (2016). The Square-Root Lasso. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_3

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