Data-driven model choice in multivariate nonparametric regression

Statistics

Volumn 36, Issue 3, 2002, Pages 231-246

  Vieu, Philippe ^a,b  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b CNRS   (France)

Author keywords

Dimensionality; Model Choice; Nonparametric Regression

Indexed keywords

EID: 0036765938     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880212857     Document Type: Article

References (42)

1. Ango-Nzé, P. and Doukhan, P. (1996) "Functional estimation for time series I: Quadratic convergence properties", Mathematical Methods of Statistics 5, 404-423.
2. Auestad, B. and Tjostheim, D. (1990) "Identification in nonlinear time series: first order characterization and order determination", Biometrika 77, 669-687.
3. Baraud, Y. (2000) "Model selection for regression on a fixed point. Proba. Theory Related Fields 117, 467-493.
4. Barron, A., Birgé, L. and Massart, P. (1999) "Risk bounds for model selection via penalization", Proba. Theory Related Fields 113, 301-413.
5. Bosq, D. (1996) Nonparametric statistics for stochastic processes: estimation and prediction. Lecture Note in Statistics, 110, Springer-Verlag.
6. Buja, A., Hastie, T. and Tibshirani, R. (1989) "Linear smoothers and additive models (with discussions)", Ann. Statist. 17, 353-455.
7. Bunke, O. (1973) "Model choice and parameter estimation in regression analysis", Math. Operationsforsch. Statist. 4, 407-423.
8. Breiman, L. and Freedman, D. (1983) "How many variables should be entered in a regression equation?", J. Amer. Statist. Assoc. 78, 131-36.
9. Breiman, L. and Spector, D. (1992) "Submodel selection and evaluation in regression", Inter. Statist. Rev. 60, 281-319.
10. Camlong, C., Sarda, P. and Vieu, Ph. (2000) "Additive time series: The kernel integration method", Mathematical Methods of Statistics, 9, 358-375.
11. Chen, Z. (1991) "Estimation of projection pursuit type regression models", Ann Statist. 19, 142-157.
12. Chen, Z. (1993) "Fitting multivariate regression functions by intraction spline models", J. Roy. Statist. Soc: B 55, 473-491.
13. Collomb, O. (1984) "Propriétés de convergence presque compléte du prédicteur à noyau", Z. Wahr, und verw. Geb. 66, 309-342.
14. Fan, J. and Li, Q. (1996) "Consistent model specification tests: Omitted variables and semiparametric functional forms", Econometrica 64, 865-890.
15. Friedmann, J. and Stuetlze, W. (1981) "Projection pursuit regression", J. Amer. Statist. Assoc. 76, 817-823.
16. Györfi, L., Härdle, W., Sarda, P. and Vieu, P. (1989) Nonparametric curve estimation from time series. Lecture Notes in Statistics, 60, Springer Verlag.
17. Hall, P. (1989) "On projection pursuit regression", Ann Statist. 17, 573-588.
18. Härdle, W., Hall, P. and Ichimura, H. (1993) "Optimal smoothing in single index models", Ann. Statist. 21, 157-178.
19. Härdle, W. and Vieu, Ph. (1992) "Kernel regression of time series", Journal of Time Series Analysis 13, 209-232.
20. Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models (Chapman and Hall, London).
21. Hidalgo, X. (1999) "Nonparametric tests for model selection with time series data", TEST 2, 365-398.
22. Koul, H.L. and Stute, W. (1999) "Nonparametric model checks for time series", Ann. of Statist. 27, 204-236.
23. Lavergne, P. and Vuong, Q.H. (1996) "Nonparametric selection of regressors: the non-nested case", Econometrica 64, 207-219.
24. Lee, G. and Hart, J. (2000) "Model selection criteria with data dependent penalty, with applications to data-driven Neyman smooth tests", J. Nonparametr. Statist. 12, 683-707.
25. Li, K.C. (1991) "Sliced inverse regression for dimension reduction (with discussions)", J. Amer. Statist. Assoc. 86, 316-342.
26. Linton, O. and Nielsen, J. (1995) "A kernel method of estimating structured nonparametric regression based on marginal integration", Biometrika 82, 93-100.
27. Lugosi, C. and Nobel, A. (1999) "Adaptive model selection using empirical complexities", Ann. Statist. 27, 1830-1864.
28. Masry, E. and Tjostheim, D. (1997) "Additive nonlinear ARX time series and projection estimates", Econometric Theory 13, 214-252.
29. Miller, A.J. (1990) Subset Selection in Regression (Chapman and Hall. London).
30. Qian, G. and Künsch, H. (1998) "On model selection via stochastich complexity in robust nonlinear regresion", J. Statist. Plann. Inference 75, 91-116.
31. Schimek, M. (2000) Smoothing and Regression: Approaches, Computation and Applications (Wiley Series in Probability and Statistics).
32. Shi, P. and Tsai, C.L. (1999) "Semiparametric regression model selections", J. Statist. Plann. Inference 11, 119-139.
33. Stone, C. (1982) "Optimal global rates of convergence for nonparametric regression", Ann. Statist. 10, 1040-1053.
34. Stone, C. (1994) "The use of polynomial splines and their tensor products in multivariate function estimiation (with discussions)", Ann. Statist. 22, 118-184.
35. Stute, W. (1997) "Nonparametric model checks for regression", Ann Statist. 25, 613-641.
36. Stute, W., Gonzalez-Manteiga, W. and Presedo-Quindimil, M. (1998) "Bootstrap approximation in model checks for regression", J. Amer. Statist. Assoc. 93, 141-149.
37. Tjostheim, D. and Auestad, B. (1994) Nonparametric identification in nonlinear time series: Projections", J. Amer. Statist. Assoc. 89, 1398-1409.
38. Vieu, P. (1991) "Quadratic errors for nonparametric estimates under dependence", J. of Multiv. Anal. 39, 324-347.
39. Vieu, P. (1994) "Choice of regressors in nonparametric estimation", Comp. Statist. Data Anal. 17, 575-594.
40. Vieu, P. (1995) "Order choice in nonlinear autoregressive models", Statistics 26, 307-328.
41. Yang, Y. (1999) "Model selection for nonparametric regression", Statistica Sinica 9, 475-499.
42. Zhang, P. (1991) "Variable selection in nonparametric regression with continuous covariates", Ann. Statist. 19, 1869-1882.