Title: Bias reduction in tail estimation and modelling a full data set
Authors: Jan Beirlant - KULeuven (Belgium) [presenting]
Abstract: In recent years several attempts have been made to model both the modal and tail part of the data. A dynamic mixture of two components with a weight function smoothly connecting the bulk and the tail of the distribution has been proposed. Recently, nice review on this topic has been made, and a new statistical model has been proposed which is in compliance with extreme value theory and allows for a smooth transition between the modal and tail part. Incorporating second order rates of convergence for distributions of peaks over thresholds, models have been constructed that can be viewed as special cases from both approaches discussed above. When fitting such second order models, it turns out that the bias of the resulting extreme value estimators is significantly reduced compared to the fit with one Pareto component. Recently, it has been shown that using penalized likelihood methods on the weight parameter one can obtain good bias and mean squared error properties for tail estimators. We encompass the above approaches providing models that can be used to model full data sets, that comply with extreme value theory, and that provide appropriate tail fits with special attention for tail estimation with reduced bias and mean squared error under the classical max-domain of attraction conditions.