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Selection of components and degrees of smoothing via lasso in high dimensional nonparametric additive models

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  • Zheng, Shurong

Abstract

This paper proposes a procedure for selecting components and degrees of smoothing in high dimensional nonparametric additive models. In the procedure, different components have different penalties, and all the smoothing parameters in one component have the same penalties. The idea is similar to, but in fact different from, Wang et al.'s [Wang, H., Li, G.D., Tsai, C.L., 2007. Regression coefficient and autoregressive order shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 69, 63-78] modified lasso, which requires different penalties for different parameters. The procedure obtains the sequence of components according to the importance of these components by Efron et al.'s [Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., 2004. Least angle regression. Annals of Statistics 32, 407-489] LARS. CV or BIC selector can be used to select the tuning parameters in the procedure, where some asymptotic properties are proved. Some simulation results and two examples are used to illustrate the procedure.

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  • Zheng, Shurong, 2008. "Selection of components and degrees of smoothing via lasso in high dimensional nonparametric additive models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 164-175, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:164-175
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    References listed on IDEAS

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    1. Gerhard Tutz & Harald Binder, 2006. "Generalized Additive Modeling with Implicit Variable Selection by Likelihood-Based Boosting," Biometrics, The International Biometric Society, vol. 62(4), pages 961-971, December.
    2. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    3. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    4. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    5. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    6. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    7. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
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    Cited by:

    1. de Uña Álvarez, Jacobo & Roca Pardiñas, Javier, 2009. "Additive models in censored regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3490-3501, July.
    2. Umberto Amato & Anestis Antoniadis & Italia De Feis, 2016. "Additive model selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 519-564, November.
    3. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.

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