KTH/CESIS Working Paper Series in Economics and Institutions of Innovation
High-dimensional CLTs for individual Mahalanobis distances
() and Deliang Dai
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; (follow links to similar papers)
JEL-Codes: C38; C46; C50; (follow links to similar papers)
13 pages, May 6, 2014
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