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Composite Quantile Regression for the Single-Index Model

Author

Listed:
  • Yan Fan
  • Wolfgang Karl Härdle
  • Weining Wang
  • Lixing Zhu

Abstract

Quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. When it comes to nonparametric specifications of the conditional quantile (or more generally tail) curve one faces, as in mean regression, a dimensionality problem. We propose a projection based single index model specifi- cation. For very high dimensional regressors X one faces yet another dimensionality problem and needs to balance precision vs. dimension. Such a balance may be achieved by combining semiparametric ideas with variable selection techniques.

Suggested Citation

  • Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2013. "Composite Quantile Regression for the Single-Index Model," SFB 649 Discussion Papers SFB649DP2013-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2013-010
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    Cited by:

    1. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.
    2. Poeschel, Friedrich, 2012. "Assortative matching through signals," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    3. Lining Yu & Wolfgang Karl Härdle & Lukas Borke & Thijs Benschop, 2017. "FRM: a Financial Risk Meter based on penalizing tail events occurrence," SFB 649 Discussion Papers SFB649DP2017-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Jing Sun, 2016. "Composite quantile regression for single-index models with asymmetric errors," Computational Statistics, Springer, vol. 31(1), pages 329-351, March.
    5. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.

    More about this item

    Keywords

    Quantile Single-index Regression; Minimum Average Contrast Estimation; Co- VaR estimation; Composite quasi-maximum likelihood estimation; Lasso; Model selection;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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