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Median Balls: An Extension of the Interquantile Intervals to Multivariate Distributions

  • Averous, Jean
  • Meste, Michel
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    For a probability distribution on a Banach space, we introduce a family of central balls, indexed by their radius, using a proximity criterion close to those defining the spatial median. It is shown that these balls possess robustness and equivariance properties similar to those of the spatial median. They provide a multivariate generalization of the real interquantile intervals and can be interpreted as trimmed regions.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 63 (1997)
    Issue (Month): 2 (November)
    Pages: 222-241

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    Handle: RePEc:eee:jmvana:v:63:y:1997:i:2:p:222-241
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    1. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    2. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    3. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
    4. Eaton, Morris L. & Perlman, Michael D., 1991. "Concentration inequalities for multivariate distributions: I. multivariate normal distributions," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 487-504, December.
    5. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    6. Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
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