Electronic Journal of Probability

Multivariate Records Based on Dominance

Hsien-Kuei Hwang and Tsung-Hsi Tsai

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We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and d-dimensional simplex. Central limit theorems with convergence rates are established when the variance tends to infinity. Effective numerical procedures are also provided for computing the variance constants to high degree of precision.

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 60, 1863-1892.

Accepted: 16 November 2010
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05 60F05 60G70

Multivariate records Pareto optimality central limit theorems Berry-Esseen bound partial orders dominance

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Hwang, Hsien-Kuei; Tsai, Tsung-Hsi. Multivariate Records Based on Dominance. Electron. J. Probab. 15 (2010), paper no. 60, 1863--1892. doi:10.1214/EJP.v15-825. https://projecteuclid.org/euclid.ejp/1464819845

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