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2010 Multivariate Records Based on Dominance
Hsien-Kuei Hwang, Tsung-Hsi Tsai
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Electron. J. Probab. 15: 1863-1892 (2010). DOI: 10.1214/EJP.v15-825

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.

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Hsien-Kuei Hwang. Tsung-Hsi Tsai. "Multivariate Records Based on Dominance." Electron. J. Probab. 15 1863 - 1892, 2010. https://doi.org/10.1214/EJP.v15-825

Information

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

zbMATH: 1225.60043
MathSciNet: MR2738341
Digital Object Identifier: 10.1214/EJP.v15-825

Subjects:
Primary: 60C05 60F05 60G70

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

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Vol.15 • 2010
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