Estimation of tail parameters with missing largest observations

Seminar in Insurance and Economics

SPEAKER: Jan Beirlant (KU Leuven).

TITLE: Estimation of tail parameters with missing largest observations.

ABSTRACT: We consider the case where an unknown number m of the highest data is missing assuming an underlying Pareto-type distribution.  We provide  solutions for estimating the extreme value index, the number of missing data and extreme quantiles. We derive an asymptotic result of the parameter estimators and an adaptive selection method for the number of top data used in the estimation is proposed for the case where all missing data are beyond the observed data.  An estimator of the number of missing extremes spread over the largest observed data is also proposed. To this purpose, we use a likelihood solution based on exponential representations of spacings between the largest observations. We also establish an effective and fast optimization procedure using regularization, and finally comment on simulation experiments. We illustrate the methodology in a practical case from the diamond mining industry, where large-carat diamonds are expected to be missing from the dataset.

This is based on joint work with Martin Bladt.

Link to Seminar in Insurance and Economics.