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Boosting additive models using component-wise P-Splines

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  • Schmid, Matthias
  • Hothorn, Torsten

Abstract

An efficient approximation of L2 Boosting with component-wise smoothing splines is considered. Smoothing spline base-learners are replaced by P-spline base-learners, which yield similar prediction errors but are more advantageous from a computational point of view. A detailed analysis of the effect of various P-spline hyper-parameters on the boosting fit is given. In addition, a new theoretical result on the relationship between the boosting stopping iteration and the step length factor used for shrinking the boosting estimates is derived.

Suggested Citation

  • Schmid, Matthias & Hothorn, Torsten, 2008. "Boosting additive models using component-wise P-Splines," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 298-311, December.
  • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:298-311
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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, December.
    2. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    3. Buhlmann P. & Yu B., 2003. "Boosting With the L2 Loss: Regression and Classification," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 324-339, January.
    4. Leitenstorfer, Florian & Tutz, Gerhard, 2007. "Knot selection by boosting techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4605-4621, May.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
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    Cited by:

    1. Hansen, Bjørn Gunnar, 2019. "CO2 – Emission, costs and capacity of different manure management practices- results from an advisory project," Agricultural Systems, Elsevier, vol. 173(C), pages 325-334.
    2. Holger Reulen & Thomas Kneib, 2016. "Boosting multi-state models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 241-262, April.
    3. Carlos A. Manzanares & Ying Jiang & Patrick Bajari, 2015. "Improving Policy Functions in High-Dimensional Dynamic Games," NBER Working Papers 21124, National Bureau of Economic Research, Inc.
    4. Souhaib Ben Taieb & Rob J Hyndman, 2014. "Boosting multi-step autoregressive forecasts," Monash Econometrics and Business Statistics Working Papers 13/14, Monash University, Department of Econometrics and Business Statistics.
    5. Nikolay Robinzonov & Gerhard Tutz & Torsten Hothorn, 2012. "Boosting techniques for nonlinear time series models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 99-122, January.
    6. Möst Lisa & Hothorn Torsten, 2015. "Conditional Transformation Models for Survivor Function Estimation," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 23-50, May.
    7. Christmann, Andreas & Hable, Robert, 2012. "Consistency of support vector machines using additive kernels for additive models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 854-873.
    8. Heikki Kauppi & Timo Virtanen, 2018. "Boosting Non-linear Predictabilityof Macroeconomic Time SeriesComplexity and benefit take-up: Empirical evidence from the Finnish homecare allowance," Discussion Papers 124, Aboa Centre for Economics.
    9. Wang Zhu, 2011. "HingeBoost: ROC-Based Boost for Classification and Variable Selection," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-30, February.
    10. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    11. Souhaib Ben Taieb & Raphael Huser & Rob J. Hyndman & Marc G. Genton, 2015. "Probabilistic time series forecasting with boosted additive models: an application to smart meter data," Monash Econometrics and Business Statistics Working Papers 12/15, Monash University, Department of Econometrics and Business Statistics.

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