Sharp deviation bounds for quadratic forms

V. Spokoiny, M. Zhilova

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)100-113
Number of pages14
JournalMathematical Methods of Statistics
Issue number2
Publication statusPublished - Apr 2013
Externally publishedYes


  • deviation bounds
  • quadratic forms


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