Sharp deviation bounds for quadratic forms

2013/02/07 by Vladimir Spokoiny, Spokoiny, Vladimir
Mathematics · #60F10 #62F10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F10 #msc:62F10

paper · pdf · doi:10.48550/arxiv.1302.1699

arxiv created 2013/02/07 · arxiv updated 2013/02/08

Abstract

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.

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