Abstract
Lower bounds for sparse quadratic forms are studied. This has its implications for effective sparsity (or compatibility constants): the effective sparsity with empirical semi-norm \(\|X \cdot \|_{n}\) is bounded in terms of the effective sparsity with theoretical semi-norm \(\|X\cdot \|\). The results are an extension of van de Geer and Muro (Electron. J. Stat. 8:3031–3061, 2014) to more general sparsity inducing norms Ω.
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References
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S. van de Geer, A. Muro, On higher order isotropy conditions and lower bounds for sparse quadratic forms. Electron. J. Stat. 8, 3031–3061 (2014)
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van de Geer, S. (2016). Lower Bounds for Sparse Quadratic Forms. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_15
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DOI: https://doi.org/10.1007/978-3-319-32774-7_15
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