The Distribution of Test Statistics for Outlier Detection in Heavy-tailed Samples
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چکیده
We investigate the asymptotic behavior of test statistics outliers for sample drawn from heavy{tailed distributions. We extend classical results of David, Hartley and Pearson (1954) and Grubbs (1969), who considered outlier test statistics for the nite{variance case, to the heavy{tailed in nite variance case. Our main result concerns the limiting distribution of n 1=2On for the outlier statistic On = max1 i nXi min1 i nXi q 1 nPni=1 Xi X 2 when the observationsXi are the domain of attraction of an {stable law. We present approximate critical values for On for nite samples using response surface methods. 1
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تاریخ انتشار 1999