Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth
AbstractA 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.
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Bibliographic InfoPaper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2008_042.
Date of creation: 2008
Date of revision:
Publication status: Published by: ECARES
Other versions of this item:
- Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010. "Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth," ULB Institutional Repository 2013/127979, ULB -- Universite Libre de Bruxelles.
- NEP-ALL-2008-12-21 (All new papers)
- NEP-ECM-2008-12-21 (Econometrics)
- NEP-FDG-2008-12-21 (Financial Development & Growth)
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- Cascos, Ignacio & López-Díaz, Miguel, 2005. "Integral trimmed regions," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 404-424, October.
- Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232.
- Gilbert W. Bassett, 2004.
"Pessimistic Portfolio Allocation and Choquet Expected Utility,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(4), pages 477-492.
- Gilbert W. Bassett Jr & Roger Koenker & Gregory Kordas, 2004. "Pessimistic portfolio allocation and Choquet expected utility," CeMMAP working papers CWP09/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130.
- Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
- Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
- Hlubinka, Daniel & Šiman, Miroslav, 2013. "On elliptical quantiles in the quantile regression setup," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 163-171.
- Lucio Sarno & Paul Schneider & Christian Wagner, 2012.
"Properties of Foreign Exchange Risk Premiums,"
Working Paper Series
10_12, The Rimini Centre for Economic Analysis.
- Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2013.
"Testing Multivariate Economic Restrictions Using Quantiles: The Example of Slutsky Negative Semidefiniteness,"
Boston College Working Papers in Economics
836, Boston College Department of Economics.
- Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2011. "Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness," CeMMAP working papers CWP14/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Zuo, Yijun, 2013. "Multidimensional medians and uniqueness," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 82-88.
- Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853.
- Marc Hallin & Zudi Lu & Davy Paindaveine & Miroslav Siman, 2012. "Local Constant and Local Bilinear Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2012-003, ULB -- Universite Libre de Bruxelles.
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