Mathematical Methods of Statistics

, Volume 22, Issue 2, pp 100–113 | Cite as

Sharp deviation bounds for quadratic forms

  • V. SpokoinyEmail author
  • M. Zhilova


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.


quadratic forms deviation bounds 

2000 Mathematics Subject Classification

primary 60F10 secondary 62F10 


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© Allerton Press, Inc. 2013

Authors and Affiliations

  1. 1.Moscow Inst. of Physics and TechnologyWeierstrass-Inst. and Humboldt Univ. BerlinBerlinGermany
  2. 2.Moscow Inst. of Physics and Technology and Weierstrass-Inst. BerlinBerlinGermany

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