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

We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of D avid et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our m ain result concerns the limiting distribution of n(-1/2)O(n) for the outlie r statistic O-n = max(1 less than or equal toi less than or equal ton) X-i - min(1 less than or equal toi less than or equal ton) X-i / root (1/n) Sigma (n)(i=1) (X-i - (X) over bar)(2) when the observations X-i are the domain of attraction of an alpha -stable law. We present approximate critical values for O-n for finite samples usin g response surface methods. (C) 2001 Elsevier Science Ltd. All rights reser ved.