A note on multivariate location and scatter statistics for sparse data sets

David E. Tyler

doi:10.1016/j.spl.2010.05.006

A note on multivariate location and scatter statistics for sparse data sets

David E. Tyler

SAS - Statistics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

For a p-dimensional data set of size np+1 in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data.

Original language	English (US)
Pages (from-to)	1409-1413
Number of pages	5
Journal	Statistics and Probability Letters
Volume	80
Issue number	17-18
DOIs	https://doi.org/10.1016/j.spl.2010.05.006
State	Published - Sep 2010

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Affine equivariance
Robust multivariate statistics
Sparse data

Access to Document

10.1016/j.spl.2010.05.006

Fingerprint Dive into the research topics of 'A note on multivariate location and scatter statistics for sparse data sets'. Together they form a unique fingerprint.

Cite this

@article{048b912206334f238ce561505fb57658,

title = "A note on multivariate location and scatter statistics for sparse data sets",

abstract = "For a p-dimensional data set of size np+1 in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data.",

keywords = "Affine equivariance, Robust multivariate statistics, Sparse data",

author = "Tyler, {David E.}",

year = "2010",

month = sep,

doi = "10.1016/j.spl.2010.05.006",

language = "English (US)",

volume = "80",

pages = "1409--1413",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier",

number = "17-18",

}

TY - JOUR

T1 - A note on multivariate location and scatter statistics for sparse data sets

AU - Tyler, David E.

PY - 2010/9

Y1 - 2010/9

N2 - For a p-dimensional data set of size np+1 in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data.

AB - For a p-dimensional data set of size np+1 in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data.

KW - Affine equivariance

KW - Robust multivariate statistics

KW - Sparse data

UR - http://www.scopus.com/inward/record.url?scp=77954533745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954533745&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2010.05.006

DO - 10.1016/j.spl.2010.05.006

M3 - Article

AN - SCOPUS:77954533745

VL - 80

SP - 1409

EP - 1413

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 17-18

ER -

A note on multivariate location and scatter statistics for sparse data sets

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Cite this