Please use this identifier to cite or link to this item: https://doi.org/10.1023/A:1012478908041
Title: On affine equivariant multivariate quantiles
Authors: Chakraborty, B. 
Keywords: Bahadur representation
L-estimates
Multivariate ranks
Q-Q plots
Quantile contour plots
Transformation-retransformation
Issue Date: 2001
Citation: Chakraborty, B. (2001). On affine equivariant multivariate quantiles. Annals of the Institute of Statistical Mathematics 53 (2) : 380-403. ScholarBank@NUS Repository. https://doi.org/10.1023/A:1012478908041
Abstract: An extension of univariate quantiles in the multivariate set-up has been proposed and studied. The proposed approach is affine equivariant, and it is based on an adaptive transformation retransformation procedure. Bahadur type linear representations of the proposed quantiles are established and consequently asymptotic distributions are also derived. As applications of these multivariate quantiles, we develop some affine equivariant quantile contour plots which can be used to study the geometry of the data cloud as well as the underlying probability distribution and to detect outliers. These quantiles can also be used to construct affine invariant versions of multivariate Q-Q plots which are useful in checking how well a given multivariate probability distribution fits the data and for comparing the distributions of two data sets. We illustrate these applications with some simulated and real data sets. We also indicate a way of extending the notion of univariate L-estimates and trimmed means in the multivariate set-up using these affine equivariant quantiles.
Source Title: Annals of the Institute of Statistical Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/105249
ISSN: 00203157
DOI: 10.1023/A:1012478908041
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