Scandinavian Working Papers in Economics

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

No 361: High-dimensional CLTs for individual Mahalanobis distances

Thomas Holgersson () and Deliang Dai ()
Additional contact information
Thomas Holgersson: Linnaeus university, Jönköping university, & Centre of Excellence for Science and Innovation Studies (CESIS), Postal: SE 551 11, , Jönköping, , Sweden
Deliang Dai: Linnaeus university, Postal: SE 351 95, , Växjö, , Sweden

Abstract: In this paper we derive central limit theorems for two different types of Mahalanobis distances in situations where the dimension of the parent variable increases proportionally with the sample size. It is shown that although the two estimators are closely related and behave similarly in nite dimensions, they have different convergence rates and are also centred at two different points in high-dimensional settings. The limiting distributions are shown to be valid under some general moment conditions and hence available in a wide range of applications.

Keywords: Mahalanobis distance; increasing dimension; weak convergence; Marcenko-Pastur distribution; outliers; Pearson family

JEL-codes: C38; C46; C50

13 pages, May 6, 2014

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