Computing multiple-output regression quantile regions
A procedure relying on linear programming techniques is developed to compute (regression) quantile regions that have been defined recently. In the location case, this procedure allows for computing halfspace depth regions even beyond dimension two. The corresponding algorithm is described in detail, and illustrations are provided both for simulated and real data. The efficiency of a Matlab implementation of the algorithm11The code can be downloaded from http://homepages.ulb.ac.be/~dpaindav. is also investigated through extensive simulations.
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References listed on IDEAS
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- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731, November.
- Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008.
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Working Papers ECARES
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- 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.
- Paindaveine, Davy & Siman, Miroslav, 2011.
"On directional multiple-output quantile regression,"
Journal of Multivariate Analysis,
Elsevier, vol. 102(2), pages 193-212, February.
- Davy Paindaveine & Miroslav Siman, 2009. "On directional multiple-output quantile regression," Working Papers ECARES 2009_011, ULB -- Universite Libre de Bruxelles.
- Lukas, Mark A. & Shi, Mingren, 2006. "Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1213-1231, November.
- Shi, Mingren & Lukas, Mark A., 2005. "Sensitivity analysis of constrained linear L1 regression: perturbations to response and predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 779-802, April.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Narula, Subhash C. & Wellington, John F., 2002. "Sensitivity analysis for predictor variables in the MSAE regression," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 355-373, August.
- 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.
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