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High-dimensional CLTs for individual Mahalanobis distances


  • Holgersson, Thomas

    (Linnaeus university, Jönköping university, & Centre of Excellence for Science and Innovation Studies (CESIS))

  • Dai, Deliang

    (Linnaeus university)


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.

Suggested Citation

  • Holgersson, Thomas & Dai, Deliang, 2014. "High-dimensional CLTs for individual Mahalanobis distances," Working Paper Series in Economics and Institutions of Innovation 361, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
  • Handle: RePEc:hhs:cesisp:0361

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    Cited by:

    1. Deliang Dai & Yuli Liang, 2021. "High-Dimensional Mahalanobis Distances of Complex Random Vectors," Mathematics, MDPI, vol. 9(16), pages 1-12, August.

    More about this item


    Mahalanobis distance; increasing dimension; weak convergence; Marcenko-Pastur distribution; outliers; Pearson family;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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