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Weighted-mean trimming of multivariate data

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  • Dyckerhoff, Rainer
  • Mosler, Karl

Abstract

A general notion of trimmed regions for empirical distributions in d-space is introduced. The regions are called weighted-mean trimmed regions. They are continuous in the data as well as in the trimming parameter. Further, these trimmed regions have many other attractive properties. In particular they are subadditive and monotone which makes it possible to construct multivariate measures of risk based on these regions. Special cases include the zonoid trimming and the ECH (expected convex hull) trimming. These regions can be exactly calculated for any dimension. Finally, the notion of weighted-mean trimmed regions extends to probability distributions in d-space, and a law of large numbers applies.

Suggested Citation

  • Dyckerhoff, Rainer & Mosler, Karl, 2011. "Weighted-mean trimming of multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 405-421, March.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:405-421
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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.
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    Cited by:

    1. Dyckerhoff, Rainer & Mosler, Karl, 2012. "Weighted-mean regions of a probability distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 318-325.
    2. Cascos, Ignacio & Ochoa, Maicol, 2021. "Expectile depth: Theory and computation for bivariate datasets," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Cascos, Ignacio & López-Díaz, Miguel, 2012. "Trimmed regions induced by parameters of a probability," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 306-318.
    4. Walter Krämer, 2016. "Walter Krämer: Interview mit Karl Mosler," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(1), pages 63-71, February.
    5. Aubin, Jean-Baptiste & Gannaz, Irène & Leoni, Samuela & Rolland, Antoine, 2022. "Deepest voting: A new way of electing," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 1-16.
    6. Bazovkin, Pavel & Mosler, Karl, 2011. "Stochastic linear programming with a distortion risk constraint," Discussion Papers in Econometrics and Statistics 6/11, University of Cologne, Institute of Econometrics and Statistics.
    7. Karl Mosler, 2023. "Representative endowments and uniform Gini orderings of multi-attribute welfare," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(1), pages 233-250, March.
    8. 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).
    9. Pavel Bazovkin & Karl Mosler, 2015. "A general solution for robust linear programs with distortion risk constraints," Annals of Operations Research, Springer, vol. 229(1), pages 103-120, June.
    10. Liu, Xiaohui & Rahman, Jafer & Luo, Shihua, 2019. "Generalized and robustified empirical depths for multivariate data," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 70-79.

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