This paper presents sharp inequalities for deviation probability of a general quadratic form of a random vector ξ 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 ξ. The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.
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Spokoiny, V., Zhilova, M. Sharp deviation bounds for quadratic forms. Math. Meth. Stat. 22, 100–113 (2013). https://doi.org/10.3103/S1066530713020026
- quadratic forms
- deviation bounds
2000 Mathematics Subject Classification
- primary 60F10
- secondary 62F10