A procedure for outlier identification in data sets from continuous distributions

We propose a procedure, based on sums of reciprocals ofp-values, for the identification of outliers in univariate or multivariate data sets coming from continuous distributions. Using results of Csörgő (1990), we find the limiting distribution of the relevant statistic for completely specified models. By simulations, we obtain approximate quantiles for the asymptotic distribution, (which does not depend on the specific model or the dimension where the data live) and for the finite sample distribution in different dimensions of our statistic when parameters are estimated, for the multivariate Gaussian model and a multivariate double exponential model with independent coordinates. Monte Carlo evaluation shows that the procedure proposed is effective in the identification of outliers, and that it is sensitive to sample size, a feature seldom found in outlier identification methods.