The Annals of Statistics

Detection of Multivariate Outliers in Elliptically Symmetric Distributions

Bimal Kumar Sinha

Full-text: Open access

Abstract

An extension of Ferguson's (Fourth Berkeley Symposium on Probability and Mathematical Statistics, 1961, Volume 1) univariate normal results and Schwager and Margolin's (1982) multivariate normal results for detection of outliers is made to the multivariate elliptically symmetric case with mean slippage. The main result can be viewed as a robustness property of the use of Mardia's multivariate kurtosis statistic as a locally optimum test statistic to detect outliers against nonnormal multivariate distributions.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1558-1565.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346813

Digital Object Identifier
doi:10.1214/aos/1176346813

Mathematical Reviews number (MathSciNet)
MR760709

Zentralblatt MATH identifier
0554.62043

JSTOR
links.jstor.org

Subjects
Primary: 62A05
Secondary: 62H15: Hypothesis testing 62H10: Distribution of statistics 62E15: Exact distribution theory

Keywords
Locally best invariant maximal invariant mean slippage multivariate kurtosis outliers robustness Wijsman's representation theorem

Citation

Sinha, Bimal Kumar. Detection of Multivariate Outliers in Elliptically Symmetric Distributions. Ann. Statist. 12 (1984), no. 4, 1558--1565. doi:10.1214/aos/1176346813. https://projecteuclid.org/euclid.aos/1176346813


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