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Exact computation of bivariate projection depth and the Stahel-Donoho estimator

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  • Zuo, Yijun
  • Lai, Shaoyong

Abstract

The idea of data depth provides a new and promising methodology for multivariate nonparametric analysis. Nevertheless, the computation of data depth and the depth function has remained as a very challenging problem which has hindered the methodology from becoming more prevailing in practice. The same is true for the powerful Stahel-Donoho (S-D) estimator. Here, we present an exact algorithm for the computation of the bivariate projection depth (PD) of data points and consequently of the S-D estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1173-1179
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    References listed on IDEAS

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    1. Ignacio Cascos & Ilya Molchanov, 2007. "Multivariate risks and depth-trimmed regions," Finance and Stochastics, Springer, vol. 11(3), pages 373-397, July.
    2. Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
    3. Peter J. Rousseeuw & Ida Ruts, 1996. "Bivariate Location Depth," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 516-526, December.
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    Cited by:

    1. Liu, Xiaohui & Zuo, Yijun & Wang, Zhizhong, 2013. "Exactly computing bivariate projection depth contours and median," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 1-11.
    2. Van Aelst, S. & Vandervieren, E. & Willems, G., 2012. "A Stahel–Donoho estimator based on huberized outlyingness," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 531-542.
    3. Zuo, Yijun, 2021. "Computation of projection regression depth and its induced median," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    4. Maicol Ochoa & Ignacio Cascos, 2022. "Data Depth and Multiple Output Regression, the Distorted M -Quantiles Approach," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    5. Zuo, Yijun, 2013. "Multidimensional medians and uniqueness," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 82-88.
    6. Shao, Wei & Zuo, Yijun, 2012. "Simulated annealing for higher dimensional projection depth," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4026-4036.

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