Geometric median and its application in the identification of multiple outliers

Keya Rani Das and A.H.M. Rahmatullah Imon

Journal of Applied Statistics, 2014, vol. 41, issue 4, 817-831

Abstract: Geometric mean (GM) is having growing and wider applications in statistical data analysis as a measure of central tendency. It is generally believed that GM is less sensitive to outliers than the arithmetic mean (AM) but we suspect likewise the AM the GM may also suffer a huge set back in the presence of outliers, especially when multiple outliers occur in a data. So far as we know, not much work has been done on the robustness issue of GM. In quest of a simple robust measure of central tendency, we propose the geometric median (GMed) in this paper. We show that the classical GM has only 0% breakdown point while it is 50% for the proposed GMed. Numerical examples also support our claim that the proposed GMed is unaffected in the presence of multiple outliers and can maintain the highest possible 50% breakdown. Later we develop a new method for the identification of multiple outliers based on this proposed GMed. A variety of numerical examples show that the proposed method can successfully identify all potential outliers while the traditional GM fails to do so.

Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2013.856385 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:41:y:2014:i:4:p:817-831

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2013.856385

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().