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On the effect of inliers on the spatial median


Brown, BM and Hall, P and Young, GA, On the effect of inliers on the spatial median, Journal of Multivariate Analysis, 63, (1) pp. 88-104. ISSN 0047-259X (1997) [Refereed Article]

DOI: doi:10.1006/jmva.1997.1691


We point out that inliers adversely affect performance of the spatial median and its generalization due to Gentleman. They are most deleterious in the case of the median itself, and in the important setting of two dimensions. There, the second term in a stochastic expansion of the median has a component with a Cauchy limiting distribution, and does not have any finite moments. This term is substantially determined by a small number of extreme, inlying data values. The implications for bootstrap methods are significant, since the bootstrap is notoriously poor in capturing properties of extremes. Indeed, the bootstrap does not accurately approximate second-order features of the distribution of the two-dimensional spatial median. We suggest a Winsorizing device for alleviating the effects of inliers. The issue of outliers is also discussed. © 1997 Academic Press.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Statistical theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Brown, BM (Dr Bruce Brown)
ID Code:12440
Year Published:1997
Web of Science® Times Cited:8
Deposited By:Mathematics
Deposited On:1997-08-01
Last Modified:2011-08-15

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