## Electronic Journal of Probability

### Multivariate Records Based on Dominance

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1464819845

Digital Object Identifier
doi:10.1214/EJP.v15-825

Mathematical Reviews number (MathSciNet)
MR2738341

Zentralblatt MATH identifier
1225.60043

Subjects
Primary: 60C05 60F05 60G70

Rights

#### Citation

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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