TITLE: Lower bounds to the accuracy of statistical inference on heavy-tailed distributions
SPEAKER: S.Y.Novak (Middlesex University)

ABSTRACT:

We deal with the problem of statistical inference on heavy-tailed distributions (HTD).
Extreme quantiles of HTD are used as measures of risk (Value-at-Risk).
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 specific way on the sample size, the tail index and the tail constant, revealing the natural normalising sequence.