Open Access
September, 1982 Detection of Multivariate Normal Outliers
Steven J. Schwager, Barry H. Margolin
Ann. Statist. 10(3): 943-954 (September, 1982). DOI: 10.1214/aos/1176345884


The general outlier problem for a multivariate normal random sample with mean slippage is defined and is shown to be invariant under a natural group of transformations. A family of maximal invariants is obtained, and the common distribution of its members is derived. The critical region for the locally best invariant test of the null hypothesis, that there are no outliers, versus the alternative hypothesis, that some outliers are present, is found. Under very general conditions, this test is equivalent to rejecting the null hypothesis whenever Mardia's multivariate sample kurtosis is sufficiently large.


Download Citation

Steven J. Schwager. Barry H. Margolin. "Detection of Multivariate Normal Outliers." Ann. Statist. 10 (3) 943 - 954, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0497.62046
MathSciNet: MR663445
Digital Object Identifier: 10.1214/aos/1176345884

Primary: 62A05
Secondary: 62C99 , 62E15 , 62H10 , 62H15

Keywords: Locally best invariant test , maximal invariant , mean slippage , multivariate kurtosis , multivariate normal distribution , Outliers

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
Back to Top