Generalized regression quantiles, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We develop a functional data analysis approach to jointly estimate a family of generalized regression quantiles. Our approach assumes that the generalized regression quantiles share some common features that can be summarized by a small number of principal component functions. The principal component functions are modeled as splines and are estimated by minimizing a penalized asymmetric loss measure. An iterative least asymmetrically weighted squares algorithm is developed for computation. While separate estimation of individual generalized regression quantiles usually suffers from large variability due to lack of sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, which is demonstrated in a simulation study. The proposed method is applied to data from 159 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations. © 2013 Springer Science+Business Media New York.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Guo and Zhou made equal contributions to the paper. Zhou's work was partially supported by NSF grant DMS-0907170. Huang's work was partially supported by NSF grants DMS-0907170, DMS-1007618, DMS-1208952, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). Guo and Hardle were supported by CRC 649 "Economic Risk", Deutsche Forschungsgemeinschaft.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.