Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables

Abstract

We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned bounds. As an example we give estimates of the excess loss in fixed design linear regression in dependent observations.

arXiv comment11 pages

References in corpus (1)

• Norms of sub-exponential random vectors

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