Non-parametric regression tests using dimension reduction techniques

Scandinavian Journal of Statistics

Volumn 35, Issue 4, 2008, Pages 719-738

  Haag, Berthold R ^a,b  

^a HypoVereinsbank ^*

^b KVW03   (Germany)

Author keywords

Bootstrap; Kernel regression; Non parametric testing; Smooth backfitting

Indexed keywords

EID: 55849087979     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00608.x     Document Type: Article

References (25)

1. Buja, A., Hastie, T. J. Tibshirani, R. J. (1989). Linear smoothers and additive models, Ann. Statist. 17, 453 555.
2. Christopeit, N. Hoderlein, S. G. N. (2006). Local partitioned regression, Econometrica 74, 787 818.
3. Dette, H. (1999). A consistent test for the functional form of a regression based on a difference of variance estimators, Ann. Statist. 27, 1012 1050.
4. Fan, J. Jiang, J. (2005). Nonparametric inference for additive models, J. Amer. Statist. Assoc. 100, 890 907.
5. Fan, J., Zhang, C. M. Zhang, J. (2001). Generalized likelihood ratio statistics and Wilks phenomenon, Ann. Statist. 29, 153 193.
6. Härdle, W. Mammen, E. (1993). Comparing nonparametric vs. parametric regression fits, Ann. Statist. 21, 1926 1947.
7. Hjellvik, V. Tjøstheim, D. (1995). Nonparametric tests of linearity for time series, Biometrika 82, 351 368.
8. Horowitz, J. L. Mammen, E. (2007). Rate-optimal estimation for a general class of non-parametric regression models with unknown link functions, Ann. Statist. 35, 2589 2619.
9. Horowitz, J. L. Spokoiny, V. G. (2001). An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative, Econometrica 69, 599 631.
10. Li, Q. Wang, S. (1998). A simple consistent bootstrap test for a parametric regression function, J. Econometrics 87, 145 165.
11. Linton, O. B. Nielsen, J. P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika 82, 93 100.
12. de Jong, P. (1987). A central limit theorem for generalized quadratic forms, Probab. Theory Related Fields 75, 261 275.
13. Mammen, E. (1993). Bootstrap and wild bootstrap for high-dimensional linear models. Ann. Statist. 21, 255 285.
14. Mammen, E., Linton, O. B. Nielsen, J. P. (1999). The existence and asymptotic properties of a backfitting projection algorithm under weak conditions, Ann. Statist. 27, 1443 1490.
15. Mammen, E. Nielsen, J. P. (2003). Generalised structured models, Biometrika 90, 551 566.
16. Mammen, E. Park, B. U. (2005). Bandwidth selection for smooth backfitting in additive models, Ann. Statist. 33, 1260 1294.
17. Nielsen, J. P. Sperlich, S. (2005). Smooth backfitting in practice, J. Roy. Statist. Soc. Ser. B Stat. Methodol. 67, 43 61.
18. Opsomer, J. D. (2000). Asymptotic properties of backfitting estimators, J. Multivariate Anal. 73, 166 179.
19. Opsomer, J. D. Ruppert, D. (1997). Fitting a bivariate additive model by local polynomial regression, Ann. Statist. 25, 186 211.
20. Powell, J. L., Stock, J. H. Stoker, T. M. (1997). Semiparametric estimation of index coefficients, Econometrica 57, 1403 1430.
21. Sperlich, S., Linton, O. B. Härdle, W. (1999). Integration and backfitting methods in additive models: finite sample properties and comparison, Test 8, 419 458.
22. Tjøstheim, D. Auestad, B. H. (1994). Nonparametric identification of nonlinear time series: projections, J. Amer. Statist. Assoc. 89, 1398 1409.
23. Yu, K., Mammen, E. Park, B. U. (2008). Smooth backfitting in generalized additive models, Ann. Statist. 36, 228 260.
24. Zheng, C. Dette, H. (2004). A power comparison between nonparametric regression tests, Statist. Probab. Lett. 66, 289 301.
25. Zheng, J. (1996). A consistent test of functional form via nonparametric estimation techniques, J. Econometrics 75, 263 290.