A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution   with an Infinite Second Moment
  We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked, in a simulation study, by four of the most popular goodness-of-fit tests for different sample sizes. Moreover, we compare, in terms of bias and mean squared error, our estimator with Peng's estimator (Peng, 2001) and we evaluate the accuracy of some resulting confidence intervals. 
Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir, Djabrane Yahia
stat.ME math.ST stat.CO stat.TH