Stellenbosch University
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Dept Statistics Seminar: Jan Beirlant (Katholieke Universiteit Leuven, Belgium)
Start: 17/02/2023, 13:00
End: 17/02/2023, 14:00
Contact:Elizna Huysamen - 021 808 3244
Location: Van der Sterr building, 2nd Floor, Room 2048

In this paper, we consider the case where an unknown number of the highest data is missing assuming an underlying Pareto-type distribution. We provide a solution for estimating the extreme value index, the number of missing data and extreme quantiles assuming that all missing data are beyond the observed data. An adaptive selection method for the number of top data used in the estimation is proposed.  We also propose an estimator of the number of missing extremes spread over the largest observed data. To this purpose, we use a likelihood solution based on exponential representations of spacings between the largest observations.

We derive an asymptotic result of the parameter estimators and comment on simulation experiments.

We illustrate the methodology in a practical case from the diamond mining industry, where large karat diamonds are expected to be missing from the dataset.