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Expected and unexpected values of Individual Mahalanobis Distances
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.ORCID iD: 0000-0002-0789-5826
Linnaeus University, School of Business and Economics, Department of Economics and Statistics. (Ctr Data Intens Sci & Applicat)
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.ORCID iD: 0000-0002-3623-5034
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 18, 8999-9006 p.Article in journal (Refereed) Published
Abstract [en]

This paper derives first-order sampling moments of individual Mahalanobis distances (MD) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second order moments are also supplied to give some additional insight to the matter.

Place, publisher, year, edition, pages
Taylor & Francis, 2017. Vol. 46, no 18, 8999-9006 p.
Keyword [en]
Increasing dimension, Mahalanobis distance, Expected values, Inverse covariance matrix
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
URN: urn:nbn:se:lnu:diva-55787DOI: 10.1080/03610926.2016.1200096ISI: 000407584900013OAI: oai:DiVA.org:lnu-55787DiVA: diva2:955750
Available from: 2016-08-26 Created: 2016-08-26 Last updated: 2017-08-31Bibliographically approved

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Dai, DeliangHolgersson, ThomasKarlsson, Peter S.
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Citation style
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