Statistics and Computing

, Volume 25, Issue 2, pp 189–202 | Cite as

Functional data analysis of generalized regression quantiles

  • Mengmeng Guo
  • Lan Zhou
  • Jianhua Z. Huang
  • Wolfgang Karl Härdle
Article

Abstract

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.

Keywords

Asymmetric loss function Functional data analysis Generalized quantiles Iteratively reweighted least squares Principal component analysis Penalized splines 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Mengmeng Guo
    • 1
  • Lan Zhou
    • 2
  • Jianhua Z. Huang
    • 2
  • Wolfgang Karl Härdle
    • 3
    • 4
  1. 1.Research Institute of Economics and ManagementSouthwestern University of Finance and EconomicsChengduChina
  2. 2.Department of StatisticsTexas A&M UniversityCollege StationUSA
  3. 3.Chair of Statistics and Center for Applied Statistics and EconomicsHumboldt-Universität zu BerlinBerlinGermany
  4. 4.Business School Quantitative FinanceSingapore Management UniversitySingaporeSingapore

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