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

S. Mittnik, S. T. Rachev, G. Samorodnitsky

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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-1/2On for the outlier statistic when the observations Xi are the domain of attraction of an α-stable law. We present approximate critical values for On for finite samples using response surface methods.

Original languageEnglish
Pages (from-to)1171-1183
Number of pages13
JournalMathematical and Computer Modelling
Volume34
Issue number9-11
DOIs
StatePublished - Sep 24 2001

Keywords

  • Financial modeling
  • Infinite variance
  • Risk management
  • Robust statistics

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