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Distribution-Function-Based Bivariate Quantiles

✍ Scribed by L.-A. Chen; A.H. Welsh

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 180 KB
Volume: 83
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.2001.2043

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce bivariate quantiles which are defined through the bivariate distribution function. This approach ensures that, unlike most multivariate medians or the multivariate M-quartiles, the bivariate quantiles satisfy an analogous property to that of the univariate quantiles in that they partition R 2 into sets with a specified probability content. The definition of bivariate quantiles leads naturally to the definition of quantities such as the bivariate median, bivariate extremes, the bivariate quantile curve, and the bivariate trimmed mean. We also develop asymptotic representations for the bivariate quantiles.

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