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CESIS - Centre of Excellence for Science and Innovation Studies, Royal Institute of Technology KTH/CESIS Working Paper Series in Economics and Institutions of Innovation

No 362:
Estimating Individual Mahalanobis Distance in High-Dimensional Data

Deliang Dai (), Thomas Holgersson () and Peter Karlsson ()

Abstract: This paper treats the problem of estimating individual Mahalanobis distances (MD) in cases when the dimension of the variable p is proportional to the sample size n. Asymptotic expected values are derived under the assumption p/n->c, 0<=c<1 for both the traditional and the leave-one-out estimators. It is shown that some estimators are asymptotically biased, but that biased corrected versions are available. Moreover, a risk function is derived for finding an optimal estimate of the inverse covariance matrix on which the MD depends. This is then used to identify the optimal estimate of the inverse covariance matrix which, unlike the standard estimator, yields efficient MD estimates over the whole range 0<=c< 1.

Keywords: Increasing dimension data; Mahalanobis distance; Inverse covariance matrix; Smoothing; (follow links to similar papers)

JEL-Codes: C38; C46; C50; (follow links to similar papers)

27 pages, May 6, 2014

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