Functional Data Analysis of Generalized Quantile Regressions

[To be revised.] Quantile and expectile regression are tail oriented conditional regression. They can be transformed as generalized quantile regression. Traditional generalized quantile regression focuses on a single curve. When more random curves are available, we can estimate the single curves jointly by using the information from all subjects instead of estimate it individually. To avoid too many parameters to estimate, we apply a novel method – functional data analysis (FDA) combining least asymmetric weighted squares (LAWS), we estimate both the mean curve as the common factor curve and the individual departure curves of the generalized quantile curves via a penalized spline smoothing. We run both simulations and real data analysis to investigate the performance of the FDA method in comparison with the traditional single curve estimation method. Taking the temperature as an example, we estimate the generalized quantile curves for the volatility of the temperature in 150 weather stations in China in 2010 to analyze the different risk drivers for the temperature.