Functional Data Analysis of Generalized Quantile Regressions
AbstractGeneralized quantile regressions, 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 quantile regressions. Our approach assumes that the generalized quantile regressions 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 quantile regressions usually suffers from large variability due to lack of suffcient data, by borrowing strength across data sets, our joint estimation approach signifcantly improves the estimation effciency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations. These curves are needed to adjust temperature risk factors so that gaussianity is achieved. The normal distribution of temperature variations is vital for pricing weather derivatives with tools from mathematical finance.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-001.
Length: 26 pages
Date of creation: Jan 2013
Date of revision:
Asymmetric loss function; Common structure; Functional data analysis; Generalized quantile curve; Iteratively reweighted least squares; Penalization;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
- C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
- Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-07 (All new papers)
- NEP-ECM-2013-01-07 (Econometrics)
- NEP-ORE-2013-01-07 (Operations Research)
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