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 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−12On 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.