The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 4 (1992), 1803-1827.
Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness
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 $d$.
Ann. Statist., Volume 20, Number 4 (1992), 1803-1827.
First available in Project Euclid: 12 April 2007
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Donoho, David L.; Gasko, Miriam. Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness. Ann. Statist. 20 (1992), no. 4, 1803--1827. doi:10.1214/aos/1176348890. https://projecteuclid.org/euclid.aos/1176348890