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Estimating the Mahalanobis distance in high-dimensional data
Linnéuniversitetet, Ekonomihögskolan (FEH), Institutionen för nationalekonomi och statistik (NS).ORCID-id: 0000-0002-0789-5826
2013 (engelsk)Konferansepaper, Poster (with or without abstract) (Annet vitenskapelig)
Abstract [en]

The Mahalanobis distance is a fundamental statistic in many fields such as Outlier detection, Normality testing and Cluster analysis. However, the standard estimator developed by Mahalanobis (1936) and Wilks (1963) is not well behaved in cases when the dimension (p) of the parent variable increases proportional to the sample size (n). This case is frequently referred to as Increasing Dimension Asymptotics (IDA). Specifically, the sample covariance matrix on which the Mahalanobis distance depends becomes degenerate under IDA settings, which in turn produce stochastically unstable Mahalanobis distances. This research project consists of several parts. It (a) shows that a previously suggested family of “improved” shrinkage estimators of the covariance matrix produce inoperable Mahalanobis distances, both under classical and increasing dimension asymptotics. It (b) develops a risk function specifically designed to assess the Mahalanobis distance and identifies good estimators thereof and (c) develops a family of resolvent-type estimators of the Mahalanobis distance. This family of estimators is shown to remain well behaved even under IDA settings. Suicient conditions for the proposed estimator to outperform the traditional estimator are also supplied. The proposed estimator is argued to be a useful tool for descriptive statistics, such as Assessment of influential values or Cluster analysis, in cases when the dimension of data is proportional to the sample size.

sted, utgiver, år, opplag, sider
2013.
HSV kategori
Forskningsprogram
Statistik
Identifikatorer
URN: urn:nbn:se:lnu:diva-40914OAI: oai:DiVA.org:lnu-40914DiVA, id: diva2:795880
Konferanse
3rd joint Statistical Meeting DAGStat, Freiburg, Germany, March 18-23, 2013
Tilgjengelig fra: 2015-03-17 Laget: 2015-03-17 Sist oppdatert: 2015-05-23bibliografisk kontrollert

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