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

We investigate the asymptotic behavior of outliers test samples statistics drawn from heavy-tailed distributions. We extend classical results of David et al. and Grubbs, 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 On = (max1≤i≤n Xi − min1≤i≤n Xi)/ √((1/n) Σi=1ⁿ (Xi − &Xmacr;)²) when the observations Xi are the domain of attraction of an ∝-stable law. We present approximate critical values for On for finite samples using response surface methods.