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• W1903051497 abstract "We prove that quadratic forms in isotropic random vectors $X$ in $mathbb{R}^n$, possessing the convex concentration property with constant $K$, satisfy the Hanson-Wright inequality with constant $CK$, where $C$ is an absolute constant, thus eliminating the logarithmic (in the dimension) factors in a recent estimate by Vu and Wang. We also show that the concentration inequality for all Lipschitz functions implies a uniform version of the Hanson-Wright inequality for suprema of quadratic forms (in the spirit of the inequalities by Borell, Arcones-Giné and Ledoux-Talagrand). Previous results of this type relied on stronger isoperimetric properties of $X$ and in some cases provided an upper bound on the deviations rather than a concentration inequality.In the last part of the paper we show that the uniform version of the Hanson-Wright inequality for Gaussian vectors can be used to recover a recent concentration inequality for empirical estimators of the covariance operator of $B$-valued Gaussian variables due to Koltchinskii and Lounici." @default.
• W1903051497 created "2016-06-24" @default.
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• W1903051497 date "2015-01-01" @default.
• W1903051497 modified "2023-10-15" @default.
• W1903051497 title "A note on the Hanson-Wright inequality for random vectors with dependencies" @default.
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• W1903051497 doi "https://doi.org/10.1214/ecp.v20-3829" @default.
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