Sharp deviation bounds for quadratic forms

Understand

This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments.

• The obtained deviation bounds are similar to the case of a Gaussian random vector.
• The results are stated under general conditions and do not suppose any special structure of the vector \(\xiv\).
• The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.