Open Access
March, 1992 Highly Efficient Estimators of Multivariate Location with High Breakdown Point
Hendrik P. Lopuhaa
Ann. Statist. 20(1): 398-413 (March, 1992). DOI: 10.1214/aos/1176348529


We propose an affine equivariant estimator of multivariate location that combines a high breakdown point and a bounded influence function with high asymptotic efficiency. This proposal is basically a location $M$-estimator based on the observations obtained after scaling with an affine equivariant high breakdown covariance estimator. The resulting location estimator will inherit the breakdown point of the initial covariance estimator and within the location-covariance model only the $M$-estimator will determine the type of influence function and the asymptotic behaviour. We prove consistency and asymptotic normality and obtain the breakdown point and the influence function.


Download Citation

Hendrik P. Lopuhaa. "Highly Efficient Estimators of Multivariate Location with High Breakdown Point." Ann. Statist. 20 (1) 398 - 413, March, 1992.


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

zbMATH: 0757.62030
MathSciNet: MR1150351
Digital Object Identifier: 10.1214/aos/1176348529

Primary: 62F35
Secondary: 62H12

Keywords: bounded influence , high breakdown point , high efficiency , multivariate location

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
Back to Top