Authors

Citation

B. Chakraborty, On multivariate median regression, BERNOULLI, 5(4), 1999, pp. 683-703

Citations number

38

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Mathematics

Journal title

BERNOULLI

ISSN journal

1350-7265
→ ACNP

Volume

5

Issue

4

Year of publication

1999

Pages

683 - 703

Database

ISI

SICI code

1350-7265(199908)5:4<683:OMMR>2.0.ZU;2-H

Abstract

An extension of the concept of least absolute deviation regression for prob
lems with multivariate response is considered. The approach is based on a t
ransformation and retransformation technique that chooses a data-driven coo
rdinate system for transforming the response vectors-and then retransforms
the estimate of the matrix of regression parameters, which is obtained by p
erforming coordinatewise least absolute deviations regression on the transf
ormed response vectors. It is shown that the estimates are equivariant unde
r non-singular linear transformations of the response vectors. An algorithm
called TREMMER (Transformation Retransformation Estimates in Multivariate
MEdian:Regression) has been suggested which adaptively chooses the optimal
data-driven coordinate system and then computes the regression estimates. W
e have also indicated how resampling techniques like the bootstrap can be u
sed to conveniently estimate the standard errors of TREMMER estimates. It i
s shown that the proposed estimate is more efficient than the non-equivaria
nt coordinatewise least absolute deviations estimate, and it out performs o
rdinary least-squares estimates in the case of heavy-tailed non-normal mult
ivariate error distributions, Asymptotic normality and some other optimalit
y properties of the estimate are also discussed. Some interesting examples
are presented to motivate the need for affine equivariant estimation in mul
tivariate median regression and to demonstrate,the performance of the propo
sed methodology.