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
208-231
Chen, L.-A.
83aa6405-0cfd-41f2-9d83-1871dd94bf60
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
2002
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), .
(doi:10.1006/jmva.2001.2043).
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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Published date: 2002
Keywords:
bivariate extreme, bivariate median, bivariate quantile, bivariate quantile curve, bivariate trimmed mean
Organisations:
Statistics
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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 Mar 2024 07:36
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Author:
L.-A. Chen
Author:
A.H. Welsh
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