An Algorithm of Nonparametric Quantile Regression.

Extreme events, such as earthquakes, tsunamis, and market crashes, can have substantial impact on social and ecological systems. Quantile regression can be used for predicting these extreme events, making it an important problem that has applications in many fields. Estimating high conditional quantiles is a difficult problem. Regular linear quantile regression uses an L ₁ loss function [Koenker in Quantile regression, Cambridge University Press, Cambridge, 2005], and the optimal solution of linear programming for estimating coefficients of regression. A problem with linear quantile regression is that the estimated curves for different quantiles can cross, a result that is logically inconsistent. To overcome the curves crossing problem, and to improve high quantile estimation in the nonlinear case, this paper proposes a nonparametric quantile regression method to estimate high conditional quantiles. A three-step computational algorithm is given, and the asymptotic properties of the proposed estimator are derived. Monte Carlo simulations show that the proposed method is more efficient than linear quantile regression method. Furthermore, this paper investigates COVID-19 and blood pressure real-world examples of extreme events by using the proposed method.