Authors: Hallin, Marc
Paindaveine, Davy
Siman, Miroslav
Title: Multivariate quantiles and multiple-output regression quantiles
Other Titles: From L_1 optimization to halfspace depth
Language (ISO): en
Abstract: A new multivariate concept of quantile, based on a directional version of Koenker and Bassett s traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version, those quantiles can be computed efficiently via linear programming techniques. Consistency, Bahadur representation and asymptotic normality results are established. Most importantly, the contours generated by those quantiles are shown to coincide with the classical halfspace depth contours associated with the name of Tukey. This relation does not only allow for efficient depth contour computations by means of parametric linear programming, but also for transferring from the quantile to the depth universe such asymptotic results as Bahadur representations. Finally, linear programming duality opens the way to promising developments in depth-related multivariate rank-based inference.
Subject Headings: halfspace depth
multivariate quantiles
quantile regression
URI: http://hdl.handle.net/2003/26494
http://dx.doi.org/10.17877/DE290R-12663
Issue Date: 2009
Appears in Collections:Sonderforschungsbereich (SFB) 823

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