Shrinkage estimation and selection for multiple functional regression

Statistica Sinica

Volumn 23, Issue 1, 2013, Pages 51-74

  Lian, Heng ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Estimation consistency; Functional linear regression; Group SCAD; Principal component analysis; Selection consistency

Indexed keywords

EID: 84884228238     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2011.160     Document Type: Article

References (36)

1. Cai, T. T. and Hall, P. (2006). Prediction in functional linear regression. Ann. Statist. 34, 2159-2179.
2. Cardot, H., Ferraty, F. and Sarda, P. (1999). Functional linear model. Statist. Probab. Lett. 45, 11-22.
3. Cardot, H. and Sarda, P. (2005). Estimation in generalized linear models for functional data via penalized likelihood. J. Multivariate Anal. 92, 24-41.
4. Carroll, R. J., Delaigle, A. and Hall, P. (2009). Nonparametric prediction in measurement error models. J. Amer. Statist. Assoc. 104, 993-1003.
5. Crambes, C., Kneip, A. and Sarda, P. (2009). Smoothing splines estimators for functional linear regression. Ann. Statist. 37, 35-72.
6. Fan, J. Q. and Li, R. Z. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96, 1348-1360.
7. Fan, J. Q. and Peng, H. (2004). Nonconcave penalized likelihood with a diverging number of parameters. Ann. Statist. 32, 928-961.
8. Fan, Y. and James, G. (2011). Functional additive regression. Technical report http://www-bcf. usc.edu/~gareth/research/FAR.pdf.
9. Ferraty, F., Mas, A. and Vieu, P. (2007). Nonparametric regression on functional data: Inference and practical aspects. Austral. N. Z. J. Statist. 49, 267-286.
10. Ferraty, F. and Vieu, P. (2002). The functional nonparametric model and application to spectrometric data. Comput. Statist. 17, 545-564.
11. Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis: Theory and Practice. Springer, New York.
12. Hall, P. and Horowitz, J. L. (2007). Methodology and convergence rates for functional linear regression. Ann. Statist. 35, 70-91.
13. Huang, J., Horowitz, J. L. and Ma, S. G. (2008). Asymptotic properties of bridge estimators in sparse high-dimensional regression models. Ann. Statist. 36, 587-613.
14. Huang, L. S. and Fan, J. Q. (1999). Nonparametric estimation of quadratic regression functionals. Bernoulli 5, 927-949.
15. James, G. M. (2002). Generalized linear models with functional predictors. J. Roy. Statist. Soc. Ser. B 64, 411-432.
16. Lian, H. (2007). Nonlinear functional models for functional responses in reproducing kernel hilbert spaces. Canad. J. Statist. 35, 597-606.
17. Liang, H. and Li, R. Z. (2009). Variable selection for partially linear models with measurement errors. J. Amer. Statist. Assoc. 104, 234-248.
18. Lin, Y. and Zhang, H. H. (2006). Component selection and smoothing in multivariate nonparametric regression. Ann. Statist. 34, 2272-2297.
19. Meinshausen, N. and Buhlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34, 1436-1462.
20. Müller, H. G. and Stadtmüller, U. (2005). Generalized functional linear models. Ann. Statist. 33, 774-805.
21. Preda, C. (2007). Regression models for functional data by reproducing kernel hilbert spaces methods. J. Statist. Plann. Inference 137, 829-840.
22. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis. Springer, New York.
23. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58, 267-288.
24. Wahba, G. (1990). Spline Models for Observational Data. Society for Industrial and Applied Mathematics, Philadelphia, PA.
25. Wang, H. S. and Leng, C. L. (2007). Unified lasso estimation by least squares approximation. J. Amer. Statist. Assoc. 102, 1039-1048.
26. Wang, H. S. and Xia, Y. C. (2009). Shrinkage estimation of the varying coefficient model. J. Amer. Statist. Assoc. 104, 747-757.
27. Wang, L. F., Chen, G. and Li, H. Z. (2007). Group scad regression analysis for microarray time course gene expression data. Bioinformatics 23, 1486-1494.
28. Wang, L. F., Li, H. Z. and Huang, J. H. Z. (2008). Variable selection in nonparametric varyingcoefficient models for analysis of repeated measurements. J. Amer. Statist. Assoc. 103, 1556-1569.
29. Yao, F., Müller, H. G. and Wang, J. L. (2005). Functional linear regression analysis for longitudinal data. Ann. Statist. 33, 2873-2903.
30. Yuan, M. and Cai, T. T. (2010). A reproducing kernel hilbert space approach to functional linear regression. Ann. Statist. 38, 3412-3444.
31. Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. Roy. Statist. Soc. Ser. B 68, 49-67.
32. Zhang, H. H. (2006). Variable selection for support vector machines via smoothing spline anova. Statist. Sinica 16, 659-674.
33. Zhao, P. and Yu, B. (2006). On model selection consistency of lasso. J. Mach. Learn. Res. 7, 2541-2563.
34. Zhu, H., Vannucci, M. and Cox, D. (2010). A bayesian hierarchical model for classification with selection of functional predictors. Biometrics 66, 463-473.
35. Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101, 1418-1429.
36. Zou, H. and Li, R. Z. (2008). One-step sparse estimates in nonconcave penalized likelihood models. Ann. Statist. 36, 1509-1533.