On multivariate Gaussian tails

被引：30

作者：

Hashorva, E ^{[1
]}

Hüsler, J ^{[1
]}

机构：

[1] Univ Bern, Dept Math Stat & Actuarial Sci, CH-3012 Bern, Switzerland

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2003年 / 55卷 / 03期

关键词：

multivariate Mills ratio; Gaussian random sequences; tail asymptotics; quadratic programming;

D O I：

10.1007/BF02517804

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let {X-n, n greater than or equal to 1} be a sequence of standard Gaussian random vectors in IRd, d greater than or equal to 2. In this paper we derive lower and upper bounds for the tail probability P{X-n > t(n)} with t(n) is an element of IRd some threshold. We improve for instance bounds on Mills ratio obtained by Savage (1962, J. Res. Nat. Bur. Standards Sect. B, 66, 9396). Furthermore, we prove exact asymptotics under fairly general conditions on both X-n and t(n), as \\t(n)\\ --> infinity where the correlation matrix Sigma(n) of X-n may also depend on n.

引用

页码：507 / 522

页数：16

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