The Annals of Applied Probability

On the variance of the number of maxima in random vectors and its applications

Zhi-Dong Bai, Chern-Ching Chao, Hsien-Kuei Hwang, and Wen-Qi Liang

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Abstract

We derive a general asymptotic formula for the variance of the number of maxima in a set of independent and identically distributed random vectors in $\mathbb{R}^d$, where the components of each vector are independently and continuously distributed. Applications of the results to algorithmic analysis are also indicated.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 3 (1998), 886-895.

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903455

Digital Object Identifier
doi:10.1214/aoap/1028903455

Mathematical Reviews number (MathSciNet)
MR1627803

Zentralblatt MATH identifier
0941.60021

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 65Y25

Keywords
Maximal points multicriterial optimization Eulerian sums

Citation

Bai, Zhi-Dong; Chao, Chern-Ching; Hwang, Hsien-Kuei; Liang, Wen-Qi. On the variance of the number of maxima in random vectors and its applications. Ann. Appl. Probab. 8 (1998), no. 3, 886--895. doi:10.1214/aoap/1028903455. https://projecteuclid.org/euclid.aoap/1028903455


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