Functional Principle Component Analysis for Generalized Quantile Regression

Abstract

Both quantile regression and expectile regression are called the generalized quantile regression. With a transformation, expectile regression is a special case of quantile regression. Traditional generalized quantile regression focuses on a single curve. When several random curves are available, we can estimate the single curves by using the information from all the observations instead of individually. With a novelty method { functional principle component analysis (FPCA) combining least asymmetric weighted squares (LAWS), we estimate both the mean curve as the common factor curve and the departure curves which measure the distance for each curve from the mean curve of the generalized quantile curves via a penalized spline smoothing. We run both simulations and real data analysis to investigate the performance of the FPCA method in comparison with the traditional single curve estimation method. Taking the temperature as an example, we estimate the generalized quantile curves for the variation of the temperature in 30 cities in Germany for 2002 and 2006 via the FPCA method to analyze the di_erent risk drivers for the temperature. ? Keywords: Least asymmetric weighted squares; Functional principle component analysis; Generalized quantile curve; Common mean curve; Penalized spline smoothing.