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The quarter median

Author

Listed:
  • Ludwig Baringhaus

    (Leibniz Universität Hannover)

  • Rudolf Grübel

    (Leibniz Universität Hannover)

Abstract

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on existence, equivariance, and asymptotic normality.

Suggested Citation

  • Ludwig Baringhaus & Rudolf Grübel, 2022. "The quarter median," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 419-458, May.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:4:d:10.1007_s00184-021-00836-z
    DOI: 10.1007/s00184-021-00836-z
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    References listed on IDEAS

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    1. Ann Mitchell, 1989. "The information matrix, skewness tensor and a-connections for the general multivariate elliptic distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 289-304, June.
    2. Masse, Jean-Claude & Plante, Jean-Francois, 2003. "A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 1-26, February.
    3. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
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