Abstract:
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We focus on the problem of the robust estimation of the tail index of a regularly varying distribution. We introduce and study a trimmed version of the Hill estimator of the tail index. It turns out that this estimator is asymptotically and nearly finite sample efficient among all unbiased estimators with a given strong upper break-down point. We also develop an automatic, data-driven procedure for the choice of trimming, which results in an adaptive estimator with nearly optimal asymptotic and finite sample properties. As a by-product we also obtain an estimate of the number of extreme outliers, relative to the tail of the distribution. The performance of the new estimators is illustrated with simulations and applied to detect heavy hitters in traffic-volume for fast 20-gigabit data streams at Merit Network.
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