Sharp deviation bounds for quadratic forms

被引：10

作者：

Spokoiny V. ^{[1
]}

Zhilova M. ^{[2
]}

机构：

[1] Moscow Inst. of Physics and Technology, Weierstrass-Inst. and Humboldt Univ. Berlin, Berlin

[2] Moscow Inst. of Physics and Technology and Weierstrass-Inst. Berlin, Berlin

来源：

Mathematical Methods of Statistics | 2013年 / 22卷 / 2期

关键词：

deviation bounds; quadratic forms;

D O I：

10.3103/S1066530713020026

中图分类号：

学科分类号：

摘要：

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. © 2013 Allerton Press, Inc.

引用

页码：100 / 113

页数：13

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