Concentration of quadratic forms under a Bernstein moment assumption

Abstract

A concentration result for quadratic form of independent subgaussian random variables is derived. If the moments of the random variables satisfy a "Bernstein condition", then the variance term of the Hanson-Wright inequality can be improved. The Bernstein condition is satisfied, for instance, by all log-concave subgaussian distributions.

This short note presents a result that initially appeared in arXiv:1410.0346v1 (see Assumption 3.3). The result was later removed from arXiv:1410.0346 and the published version https://projecteuclid.org/euclid.aos/1519268423 due to space constraints

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