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
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- 1.
In this subsection \(\hat{\varSigma }\) is not the Gram matrix X T X∕n.
References
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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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DOI: https://doi.org/10.1007/978-3-319-32774-7_3
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