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Optimal expectile smoothing

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 12 (October)
    Pages: 4168-4177

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4168-4177

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    References

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275.
    2. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
    6. 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.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
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    Cited by:
    1. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    2. 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.
    3. 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.
    4. 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.

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