Automatic model selection for partially linear models

Journal of Multivariate Analysis

Volumn 100, Issue 9, 2009, Pages 2100-2111

  Ni, Xiao ^a   Zhang, Hao Helen ^a   Zhang, Daowen ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Semiparametric regression; Smoothing splines; Smoothly clipped absolute deviation; Variable selection

Indexed keywords

EID: 68949215515     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2009.06.009     Document Type: Article

References (36)

1. Hastie T., and Tibshirani R.J. Generalized Additive Models (1990), Chapman and Hall, London
2. Speckman P. Kernel smoothing in partial linear models. Journal of the Royal Statistical Society Series B 50 (1988) 413-436
3. Engle R., Granger C., Rice J., and Weiss A. Nonparametric estimates of the relation between weather and electricity sales. Journal of American Statistical Association 81 (1986) 310-386
4. Heckman N.E. Spline smoothing in a partly linear model. Journal of the Royal Statistical Society Series B 48 (1986) 244-248
5. Wahba G. Spline Models for Observation Data (1990), Society for Industrial and Applied Mathematics
6. Green P.J., and Silverman B.W. Nonparametric Regression and Generalized Linear Models (1994), Chapman and Hall, London
7. Gu C. Smoothing Spline ANOVA Models (2002), Springer, New York
8. Ruppert D., Wand M.P., and Carroll R.J. Semiparametric Regression (2003), Cambridge University Press, Cambridge, New York
9. Liang H. Estimation in partially linear models and numerical comparisons. Computational Statistics and Data Analysis 50 (2006) 675-687
10. Breiman L. Better subset selection using the nonnegative garrote. Technometrics 37 (1995) 373-384
11. Tibshirani R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B 58 (1996) 267-288
12. Fan J., and Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association 96 (2001) 1348-1360
13. Efron B., Hastie T., Johnstone I., and Tibshirani R. Least angle regression. Annals of Statistics 32 (2004) 407-451
14. Zou H. The adaptive lasso and its oracle properties. Journal of American Statistical Association 101 (2006) 1418-1429
15. Zhang H., and Lu W. Adaptive lasso for cox's proportional hazards model. Biometrika 94 (2007) 691-703
16. p. Technometrics 15 (1973) 661-675
17. Akaike H. Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika 60 (1973) 255-265
18. Schwarz G. Estimating the dimension of a model. Annals of Statistics 6 (1978) 461-464
19. Linhart H., and Zucchini W. Model Selection (1986), Wiley, New York
20. Miller A.J. Subset Selection in Regression (2002), Chapman and Hall, London
21. Fan J., and Li R. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of American Statistical Association 99 (2004) 710-723
22. Bunea F. Consistent covariate selection and post model selection inference in semiparametric regression. Annals of Statistics 32 (2004) 898-927
23. Bunea F., and Wegkamp M. Two-stage model detection procedures in partially linear regression. The Canadian Journal of Statistics 32 (2004) 105-118
24. Fan J., and Peng H. Nonconcave penalized likelihood with a diverging number of parameters. Annals of Statistics 32 (2004) 928-961
25. Xie H., and Huang J. SCAD-penalized regression in high-dimensional partially linear models. Annals of Statistics 37 (2009) 673-696
26. Huber P. Robust regression: Asymptotics, conjectures and Monte Carlo. Annals of Statistics 1 (1973) 799-821
27. Craven P., and Wahba G. Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerishe Mathematik 31 (1979) 377-403
28. Zhang D., Lin X., Raz J., and Sowers M. Semiparametric stochastic mixed models for longitudinal data. Journal of American Statistical Association 93 (1998) 710-719
29. Green P.J. Penalized likelihood for general semi-parametric regression models. International Statistical Review 55 (1987) 245-260
30. Wahba G. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Annals of Statistics 13 (1985) 1378-1402
31. Speed T. Discussion of 'blup is a good thing: The estimation of random effects' by G.K. Robinson. Statistical Science 6 (1991) 15-51
32. Wang H., Li R., and Tsai C.L. Tuning parameter selector for SCAD. Biometrika 94 (2007) 553-568
33. Wahba G. Bayesian 'confidence intervals' for the cross-validated smoothing spline. Journal of the Royal Statistical Society Series B 45 (1983) 133-150
34. Ruppert D., Sheather S., and Wand M. An effective bandwidth selector for local least squares regression. Journal of American Statistical Association 90 (1995) 1257-1270
35. Ravikumar P., Liu H., Lafferty J., and Wasserman L. Spam: Sparse additive models. Advances in Neural Information Processing Systems 20 (2008) 1202-1208
36. L. Meier, S. Van de Geer, P. Bühlmann, High-dimensional additive modeling, http://arxiv.org/abs/0806.4115v1, 2008