A1886
Title: Probability density estimators for tail-weighted mean integrated squared error
Authors: Yusuke Omura - Yokohama City University (Japan) [presenting]
Taku Moriyama - Yokohama City University (Japan)
Abstract: Large-scale risks often arise from heavy-tailed distributions, making accurate density estimation in the tail crucial for appropriate risk management decisions. A loss function for parameter selection in density estimation when large-scale risk management is the objective is proposed. A tail-weighted mean integrated squared error (WMISE) is introduced, given by an integral of the tail-weighted mean squared error. The kernel density estimator (KDE) is a common density estimator whose accuracy depends strongly on bandwidth selection. Cross-validation and plug-in criteria based on WMISE are developed to select the bandwidth. Additionally, the Hall-type estimator is considered as an existing tail density estimator. For this estimator, the optimal parameter of a tail-weighted maximum log-likelihood estimator (WMLE) is introduced in terms of WMISE under correct model specification. The behavior of the proposed bandwidth and WMISE is investigated analytically and numerically. The performances of the KDE and the Hall-type estimator with proposed and existing parameter selection methods are compared through both analytical and numerical results.
