Exactly computing bivariate projection depth contours and median
Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising center-outward ordering of multi-dimensional data. However, their further applications have been severely hindered due to their computational challenge in practice. In this paper, we derive a simple form of the projection depth function, when (μ,σ)= (Med, MAD). This simple form enables us to extend the existing result of point-wise exact computation of projection depth (PD) of Zuo and Lai (2011) to depth contours and median for bivariate data.
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- 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.
- Ruts, Ida & Rousseeuw, Peter J., 1996. "Computing depth contours of bivariate point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 153-168, November.
- Bazovkin, Pavel & Mosler, Karl, 2012. "An Exact Algorithm for Weighted-Mean Trimmed Regions in Any Dimension," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i13).
- Bazovkin, Pavel & Mosler, Karl, 2010. "An exact algorithm for weighted-mean trimmed regions in any dimension," Discussion Papers in Econometrics and Statistics 6/10, University of Cologne, Institute of Econometrics and Statistics.
- Davy Paindaveine & Miroslav Šiman, 2012. "Computing multiple-output regression quantile regions from projection quantiles," Computational Statistics, Springer, vol. 27(1), pages 29-49, March.
- Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
- Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853. Full references (including those not matched with items on IDEAS)
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