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SEMINARS |
Seminar on Probability Theory and Mathematical Statistics
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Lower bounds to the accuracy of tail index estimation S. Yu. Novak |
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Abstract: We deal with the problem of statistical inference on heavy-tailed distributions. We present non-uniform minimax lower bounds to the mean squared error (MSE) of tail index and extreme quantiles estimators. We show that the MSE of a robust estimator depends in a particular way on the sample size, the tail index and the tail constant, revealing the the natural normalising sequence. |