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Asymptotics for the Tukey Median

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  • Massé, Jean-Claude

Abstract

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a bivariate setting and by Bai and He in the general multivariate case. To establish their theorem, these authors made a strong symmetry hypothesis on the distribution and, in the case of Bai and He, assumed the existence of a density function with a gradient satisfying a finite-moment condition. This paper extends the above result by deriving the asymptotic distribution of the above location estimate without making any symmetry or differentiability assumption on the distribution.

Suggested Citation

  • Massé, Jean-Claude, 2002. "Asymptotics for the Tukey Median," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 286-300, May.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:2:p:286-300
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    References listed on IDEAS

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    1. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    2. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
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    Cited by:

    1. Ryan Cumings-Menon, 2022. "Differentially Private Estimation via Statistical Depth," Papers 2207.12602, arXiv.org.

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