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Distribution-function-based bivariate quantiles

Distribution-function-based bivariate quantiles
Distribution-function-based bivariate quantiles
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 R2 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.
bivariate extreme, bivariate median, bivariate quantile, bivariate quantile curve, bivariate trimmed mean
0047-259X
208-231
Chen, L.-A.
83aa6405-0cfd-41f2-9d83-1871dd94bf60
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Chen, L.-A.
83aa6405-0cfd-41f2-9d83-1871dd94bf60
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a

Chen, L.-A. and Welsh, A.H. (2002) Distribution-function-based bivariate quantiles. Journal of Multivariate Analysis, 83 (1), 208-231. (doi:10.1006/jmva.2001.2043).

Record type: Article

Abstract

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 R2 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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More information

Published date: 2002
Keywords: bivariate extreme, bivariate median, bivariate quantile, bivariate quantile curve, bivariate trimmed mean
Organisations: Statistics

Identifiers

Local EPrints ID: 29941
URI: http://eprints.soton.ac.uk/id/eprint/29941
ISSN: 0047-259X
PURE UUID: 3104b8b2-541d-4fec-bb12-6bd400a98db6

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Date deposited: 12 May 2006
Last modified: 15 Jul 2019 19:08

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