Abstract
This chapter presents probability inequalities for the (dual) norm of a Gaussian vector in \(\mathbb{R}^{p}\). For Gaussian vectors there are ready-to-use concentration Borell, C. inequalities (e.g. Borell, 1975). Here however, results are derived using direct arguments. The extension to for example sub-Gaussian vectors is then easier to read off. Bounds for the supremum are given, for the ℓ 2-norm, and more generally for dual norms of norms generated from a convex cone.
Keywords
- Convex Cone
- Moment Generate Function
- Gaussian Vector
- Dual Norm
- Standard Normal Random Variable
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van de Geer, S. (2016). Empirical Process Theory for Dual Norms. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_8
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DOI: https://doi.org/10.1007/978-3-319-32774-7_8
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