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Finite sample tail behavior of multivariate location estimators

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  • Zuo, Yijun

Abstract

A finite sample performance measure of multivariate location estimators is introduced based on "tail behavior". The tail performance of multivariate "monotone" location estimators and the halfspace depth based "non-monotone" location estimators including the Tukey halfspace median and multivariate L-estimators is investigated. The connections among the finite sample performance measure, the finite sample breakdown point, and the halfspace depth are revealed. It turns out that estimators with high breakdown point or halfspace depth have "appealing" tail performance. The tail performance of the halfspace median is very appealing and also robust against underlying population distributions, while the tail performance of the sample mean is very sensitive to underlying population distributions. These findings provide new insights into the notions of the halfspace depth and breakdown point and identify the important role of tail behavior as a quantitative measure of robustness in the multivariate location setting.

Suggested Citation

  • Zuo, Yijun, 2003. "Finite sample tail behavior of multivariate location estimators," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 91-105, April.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:91-105
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    References listed on IDEAS

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    1. Zuo, Yijun & Serfling, Robert, 2000. "Nonparametric Notions of Multivariate "Scatter Measure" and "More Scattered" Based on Statistical Depth Functions," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 62-78, October.
    2. Jurecková, Jana, 2000. "Test of tails based on extreme regression quantiles," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 53-61, August.
    3. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
    4. Jozef Kušnier & Ivan Mizera, 2001. "Tail Behavior and Breakdown Properties of Equivariant Estimators of Location," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 244-261, June.
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