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Optimal expectile smoothing

Author

Listed:
  • Schnabel, Sabine K.
  • Eilers, Paul H.C.

Abstract

Quantiles are computed by optimizing an asymmetrically weighted L1 norm, i.e. the sum of absolute values of residuals. Expectiles are obtained in a similar way when using an L2 norm, i.e. the sum of squares. Computation is extremely simple: weighted regression leads to the global minimum in a handful of iterations. Least asymmetrically weighted squares are combined with P-splines to compute smooth expectile curves. Asymmetric cross-validation and the Schall algorithm for mixed models allow efficient optimization of the smoothing parameter. Performance is illustrated on simulated and empirical data.

Suggested Citation

  • Schnabel, Sabine K. & Eilers, Paul H.C., 2009. "Optimal expectile smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4168-4177, October.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4168-4177
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, April.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
    4. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, April.
    6. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    7. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
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    Citations

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    Cited by:

    1. Sabine K. Schnabel & Paul Eilers, 2009. "An analysis of life expectancy and economic production using expectile frontier zones," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 21(5), pages 109-134, August.
    2. Luciano Stefanini, 2015. "Quantile and expectile smoothing by F-transform," Working Papers 1512, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2015.
    3. Luciano Stefanini & Maria Letizia Guerra, 2013. "Fuzzification via F-transform," Working Papers 1310, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2013.
    4. Stephan Stahlschmidt & Matthias Eckardt & Wolfgang K. Härdle, 2014. "Expectile Treatment Effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers SFB649DP2014-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. repec:eee:csdana:v:116:y:2017:i:c:p:49-66 is not listed on IDEAS
    6. repec:eee:stapro:v:137:y:2018:i:c:p:304-311 is not listed on IDEAS
    7. P. Burdejova & W.K. Härdle & Kokoszka & Q.Xiong, 2015. "Change point and trend analyses of annual expectile curves of tropical storms," SFB 649 Discussion Papers SFB649DP2015-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    9. Huang, Xiaolin & Shi, Lei & Suykens, Johan A.K., 2014. "Asymmetric least squares support vector machine classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 395-405.
    10. Farooq, Muhammad & Steinwart, Ingo, 2017. "An SVM-like approach for expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 159-181.
    11. repec:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0741-3 is not listed on IDEAS
    12. Voudouris, Vlasios & Matsumoto, Ken'ichi & Sedgwick, John & Rigby, Robert & Stasinopoulos, Dimitrios & Jefferson, Michael, 2014. "Exploring the production of natural gas through the lenses of the ACEGES model," Energy Policy, Elsevier, vol. 64(C), pages 124-133.
    13. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.

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