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December, 1992 Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness
David L. Donoho, Miriam Gasko
Ann. Statist. 20(4): 1803-1827 (December, 1992). DOI: 10.1214/aos/1176348890

Abstract

We describe multivariate generalizations of the median, trimmed mean and $W$ estimates. The estimates are based on a geometric construction related to "projection pursuit." They are both affine equivariant (coordinate-free) and have high breakdown point. The generalization of the median has a breakdown point of at least $1/(d + 1)$ in dimension $d$ and the breakdown point can be as high as $1/3$ under symmetry. In contrast, various estimators based on rejecting apparent outliers and taking the mean of the remaining observations have breakdown points not larger than $1/(d + 1)$ in dimension $d$.

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David L. Donoho. Miriam Gasko. "Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness." Ann. Statist. 20 (4) 1803 - 1827, December, 1992. https://doi.org/10.1214/aos/1176348890

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0776.62031
MathSciNet: MR1193313
Digital Object Identifier: 10.1214/aos/1176348890

Subjects:
Primary: 62F35
Secondary: 62G05, 62H12

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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