High quantile regression for extreme events.

For extreme events, estimation of high conditional quantiles for heavy tailed distributions is an important problem. Quantile regression is a useful method in this field with many applications. Quantile regression uses an L ₁-loss function, and an optimal solution by means of linear programming. In this paper, we propose a weighted quantile regression method. Monte Carlo simulations are performed to compare the proposed method with existing methods for estimating high conditional quantiles. We also investigate two real-world examples by using the proposed weighted method. The Monte Carlo simulation and two real-world examples show the proposed method is an improvement of the existing method.