Finite sample tail behavior of multivariate location estimators |
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Authors: | Yijun Zuo |
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Affiliation: | a Department of Statistics and Probability, Michigan State University, A440 Wells Hall, East Lansing, MI 48824, USA b Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA |
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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. |
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Keywords: | primary 62F12 secondary 62G35 62H12 |
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