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 W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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- 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.
- 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.
- 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.
- Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
- Davy Paindaveine & Miroslav Siman, 2009.
"On directional multiple-output quantile regression,"
Working Papers ECARES
2009_011, 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.
- 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.
- 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.
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