Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables
arXiv:1809.08569 · doi:10.1016/j.spl.2020.108898
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.
11 pages