Linear or nonlinear? automatic structure discovery for partially linear models

Journal of the American Statistical Association

Volumn 106, Issue 495, 2011, Pages 1099-1112

  Zhang, Hao Helen ^a,b   Cheng, Guang ^c   Liu, Yufeng ^d  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b The University of Arizona   (United States)

^c PURDUE UNIVERSITY   (United States)

^d University of North Carolina at Chapel Hill   (United States)

Author keywords

Model selection; RKHS; Semiparametric regression; Shrinkage; Smoothing splines

Indexed keywords

EID: 80054678826     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2011.tm10281     Document Type: Article

References (36)

1. Agmon, S. (1965), Lectures on Elliptic Boundary Value Problems, Princeton, NJ: van Nostrand. [1110]
2. p, " Mathematics of the USSR Sbornik, 73, 295-317. [1110]
3. Chen, H. (1988), "Convergence Rates for Parametric Components in a Partly Linear Model, " The Annals of Statistics, 16, 136-146. [1099]
4. Dinse, G. E., and Lagakos, S. W. (1983), "Regression Analysis of Tumour Prevalence Data, " Journal of the Royal Statistical Society, Ser. C, 32, 236-248. [1099]
5. Engle, R., Granger, C., Rice, J., and Weiss, A. (1986), "Semiparametric Estimates of the Raltion BetweenWeather and Electricity Sales, " Journal of the American Statistical Association, 81, 310-386. [1099]
6. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall. [1099]
7. Fan, J., and Jinchi, L. (2008), "Sure Independence Screening for Ultrahigh Dimensional Feature Space, " Journal of the Royal Statistical Society, Ser. B, 70, 849-911. [1109]
8. Fan, J., and Li, R. (2004), "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis, " Journal of the American Statistical Association, 99, 710-723. [1099]
9. Fan, J., Feng, Y., and Song, R. (2011), "Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models, " Journal of the American Statistical Association, 106, 544-557. [1109]
10. Green, P. J., and Silverman, B.W. (1994), Nonparametric Regression and Generalized Linear Models, London: Chapman & Hall. [1099]
11. Gu, C. (2002), Smoothing Spline ANOVA Models, New York: Springer-Verlag. [1100,1103]
12. Hardle, W., Liang, H., and Gao, J. (2000), Partially Linear Models, Heidelberg: Physica-Verlag. [1099]
13. Heckman, N. E. (1986), "Spline Smoothing in a Partly Linear Model, " Journal of the Royal Statistical Society, Ser. B, 48, 244-248. [1099]
14. Hong, S. Y. (1991), "Estimation Theory of a Class of Semiparametric Regression Models, " Sciences in China Ser. A, 12, 1258-1272. [1099]
15. Huang, J., Horowitz, J., and Wei, F. (2010), "Variable Selection in Nonparametric Additive Models, " The Annals of Statistics, 38, 2282-2313. [1109]
16. Kimeldorf, G., and Wahba, G. (1971), "Some Results on Tchebycheffian Spline Functions, " Journal of Mathematical Analysis and Applications, 33, 82-85. [1103]
17. Li, R., and Liang, H. (2008), "Variable Selection in Semiparametric Regression Modeling, " The Annals of Statistics, 36, 261-286. [1099]
18. Liang, H. (2006), "Estimation in Partially Linear Models and Numerical Comparisons, " Computational Statistics and Data Analysis, 50, 675-687. [1099]
19. Liang, H., Hardle, W., and Carroll, R. J. (1999), "Estimation in a Semiparametric Partially Linear Errors-in-VariablesModel, " The Annals of Statistics, 27, 1519-1535. [1099]
20. Lin, Y., and Zhang, H. H. (2006), "Component Selection and Smoothing in Multivariate Nonparametric Regression, " The Annals of Statistics, 34, 2272-2297. [1101,1102]
21. Mammen, E., and van de Geer, S. (1997), "Penalized Quasi-Likelihood Estimation in Partial Linear Models, " The Annals of Statistics, 25, 1014-1035. [1103,1110,1111]
22. Ravikumar, P., Lafferty, J., Liu, H., and Wasserman, L. (2009), "Sparse Additive Models, " Journal of the Royal Statistical Society, Ser. B, 71, 1009-1030. [1109]
23. Rice, J. (1986), "Convergence Rates for Partially SplineModels, " Statistics and Probability Letters, 4, 203-208. [1099]
24. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge: Cambridge University Press. [1099]
25. Schmalensee, R., and Stoker, T. M. (1999), "Household Gasoline Demand in the United States, " Econometrica, 67, 645-662. [1099]
26. Speckman, P. (1988), "Kernel Smoothing in Partial Linear Models, " Journal of the Royal Statistical Society, Ser. B, 50, 413-436. [1099]
27. Storlie, C., Bondell, H., Reich, B., and Zhang, H. H. (2011), "Surface Estimation, Variable Selection, and the Nonparametric Oracle Property, " Statistica Sinica, 21, 679-705. [1101]
28. Tibshirani, R. J. (1996), "Regression Shrinkage and Selection via the Lasso, " Journal of the Royal Statistical Society, Ser. B, 58, 267-288. [1101]
29. van de Geer, S. (2000), Empirical Processes in M-Estimation, Cambridge: Cambridge University Press. [1110,1111]
30. Wahba, G. (1984), "Cross Validated Spline Methods for the Estimation of Multivariate Functions From Data on Functions, Statistics: An Appraisal, " in Proceedings 50th Anniversary Conference Iowa State Statistical Laboratory, ed. H. A. David, Ames, IA: Iowa State University Press, pp. 205-235. [1099]
31. Wahba, G. (1990), Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 59, Philadelphia: SIAM. [1100,1103]
32. Wang, H., Li, G., and Jiang, G. (2007), "Robust Regression Shrinkage and Consistent Variable Selection via the Lad-Lasso, " Journal of Business & Economic Statistics, 20, 347-355. [1101]
33. Wang, L., Li, H., and Huang, J. (2008), "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements, " Journal of the American Statistical Association, 103, 1556-1569. [1099]
34. Zhang, H. H., and Lin, Y. (2006), "Component Selection and Smoothing for Nonparametric Regression in Exponential Families, " Statistica Sinica, 16, 1021-1042. [1101]
35. Zhang, H. H., and Lu, W. (2007), "Adaptive-Lasso for Cox's Proportional Hazards Model, " Biometrika, 94, 691-703. [1101]
36. Zou, H. (2006), "The Adaptive Lasso and Its Oracle Properties, " Journal of the American Statistical Association, 101, 1418-1429. [1101]