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Sharp deviation bounds for quadratic forms


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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Correspondence to V. Spokoiny.

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Spokoiny, V., Zhilova, M. Sharp deviation bounds for quadratic forms. Math. Meth. Stat. 22, 100–113 (2013).

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  • quadratic forms
  • deviation bounds

2000 Mathematics Subject Classification

  • primary 60F10
  • secondary 62F10