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.

中文翻译：

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次高斯相关随机变量中二次形式的尾部概率的界限

摘要 我们展示了次高斯非必要独立随机变量中二次形式的尾部概率的界限。我们的主要工具将是对此类形式的卢森堡规范的估计。这将使我们能够制定上述界限。作为一个例子，我们在非独立观察中给出了固定设计线性回归中超额损失的估计。