Selection of components and degrees of smoothing via lasso in high dimensional nonparametric additive models
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 etÂ 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 etÂ 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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- Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
- 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.
- 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.
- 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.
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