KTH/CESIS Working Paper Series in Economics and Institutions of Innovation
Estimating Individual Mahalanobis Distance in High-Dimensional Data
(), 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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