Projection estimates of multivariate location.

JORGE G. ADROVER AND VICTOR J. YOHAI

ANNALS OF STATISTICS, THE

INST MATHEMATICAL STATISTICS

Año: 2002 vol. 30 p. 1760 - 1781

0090-5364

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 distributionst he maximumb ias of this estimated ependso nly 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.