The distribution of test statistics for outlier detection in heavy-tailed samples

  • Authors:

  • S. Mittnik;S. T. Rachev;G. Samorodnitsky

  • Affiliations:

  • Institute of Statistics and Econometrics University of Kiel Olshausenstr. 40, D-24098 Kiel, Germany;Institute of Statistics and Mathematical Economics University of Karlsruhe Kollegium am Schloss Bau II, D-76128 Karlsruhe, Germany;School of Operations Research and Industrial Engineering Cornell University Rhodes Hall, Ithaca, NY 14853-3801, U.S.A.

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2001

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Abstract

We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n^-^1^2O"n for the outlier statistic when the observations X"i are the domain of attraction of an @a-stable law. We present approximate critical values for O"n for finite samples using response surface methods.