Annals of Statistics

Some inequalities for symmetric convex sets with applications

T. W. Anderson

Full-text: Open access

Abstract

Under appropriate conditions the probability of a convex symmetric set decreases as the spread or scatter of the distribution increases. This paper studies the conditions when the random vector has a symmetric unimodal distribution.

Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 753-762.

Dates
First available in Project Euclid: 24 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032894463

Digital Object Identifier
doi:10.1214/aos/1032894463

Mathematical Reviews number (MathSciNet)
MR1394986

Zentralblatt MATH identifier
0865.60009

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60E15: Inequalities; stochastic orderings 62H15: Hypothesis testing

Keywords
Convex sets inequalities unimodal functions elliptically contoured distributions monotonicity of power functions

Citation

Anderson, T. W. Some inequalities for symmetric convex sets with applications. Ann. Statist. 24 (1996), no. 2, 753--762. doi:10.1214/aos/1032894463. https://projecteuclid.org/euclid.aos/1032894463


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References

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