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December 2002 Projection estimates of multivariate location
Jorge Adrover, Víctor Yohai
Ann. Statist. 30(6): 1760-1781 (December 2002). DOI: 10.1214/aos/1043351256

Abstract

In this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion. In particular we study the projection estimate that uses the median and median absolute deviation about the median (MAD) as univariate location and dispersion estimates respectively. This estimator may be considered a natural affine equivariant multivariate median. For spherical distributions the maximum bias of this estimate depends only on the marginal distributions, and not on the dimension, and is approximately twice the maximum bias of the univariate median. We also show that for multivariate normal distributions, its maximum bias compares favorably with those of the Donoho-Stahel, minimum volume ellipsoid and minimum covariance determinant estimates. In all these cases the maximum bias increases with the dimension p.

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Jorge Adrover. Víctor Yohai. "Projection estimates of multivariate location." Ann. Statist. 30 (6) 1760 - 1781, December 2002. https://doi.org/10.1214/aos/1043351256

Information

Published: December 2002
First available in Project Euclid: 23 January 2003

zbMATH: 1015.62057
MathSciNet: MR1969449
Digital Object Identifier: 10.1214/aos/1043351256

Subjects:
Primary: 62F35
Secondary: 62H12

Keywords: maximum bias , multivariate location , Projection estimates , Robust estimates

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 6 • December 2002
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