The Annals of Statistics

Asymptotic Behaviour of $S$-Estimates of Multivariate Location Parameters and Dispersion Matrices

P. L. Davies

Full-text: Open access

Abstract

It is shown under appropriate conditions that Rousseeuw's minimum volume estimator and other $S$-estimators of multivariate location and dispersion parameters are consistent. Under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of $n^{1/2}$.

Article information

Source
Ann. Statist. Volume 15, Number 3 (1987), 1269-1292.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350505

Digital Object Identifier
doi:10.1214/aos/1176350505

Mathematical Reviews number (MathSciNet)
MR902258

Zentralblatt MATH identifier
0645.62057

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62E20: Asymptotic distribution theory 62H99: None of the above, but in this section

Keywords
$S$-estimators multivariate location and dispersion parameters consistency asymptotic normality finite sample breakdown points random search

Citation

Davies, P. L. Asymptotic Behaviour of $S$-Estimates of Multivariate Location Parameters and Dispersion Matrices. Ann. Statist. 15 (1987), no. 3, 1269--1292. doi:10.1214/aos/1176350505. http://projecteuclid.org/euclid.aos/1176350505.


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