Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1457-1473 |
| Seitenumfang | 17 |
| Fachzeitschrift | Annals of Statistics |
| Jahrgang | 24 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - Aug. 1996 |
Abstract
The coordinatewise median of a multivariate data set is a highly robust location estimator, but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper we introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal transformations. We investigate the asymptotic behavior of this estimator and compare it to the spatial median.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Statistik und Wahrscheinlichkeit
- Entscheidungswissenschaften (insg.)
- Statistik, Wahrscheinlichkeit und Ungewissheit
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Annals of Statistics, Jahrgang 24, Nr. 4, 08.1996, S. 1457-1473.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Orthogonalization of multivariate location estimators
T2 - The orthomedian
AU - Grübel, Rudolf
PY - 1996/8
Y1 - 1996/8
N2 - The coordinatewise median of a multivariate data set is a highly robust location estimator, but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper we introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal transformations. We investigate the asymptotic behavior of this estimator and compare it to the spatial median.
AB - The coordinatewise median of a multivariate data set is a highly robust location estimator, but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper we introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal transformations. We investigate the asymptotic behavior of this estimator and compare it to the spatial median.
KW - Asymptotic normality
KW - Multivariate median
KW - Orthogonal equivariance
KW - Robust estimation
UR - http://www.scopus.com/inward/record.url?scp=0040159656&partnerID=8YFLogxK
U2 - 10.1214/aos/1032298277
DO - 10.1214/aos/1032298277
M3 - Article
AN - SCOPUS:0040159656
VL - 24
SP - 1457
EP - 1473
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 4
ER -