Estimation and testing for varying coefficients in additive models with marginal integration

Journal of the American Statistical Association

Volumn 101, Issue 475, 2006, Pages 1212-1227

  Yang, Lijian ^a   Park, Byeong U ^b   Lan, X U E ^c   Härdle, Wolfgang ^d  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b Seoul National University   (South Korea)

^c OREGON STATE UNIVERSITY   (United States)

^d HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Equivalent kernels; German real GNP; Local polynomial; Marginal integration; Rale of convergence

Indexed keywords

EID: 33748855347     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000000429     Document Type: Review

References (35)

1. Bosq, D. (1998), Nonparametric Statistics for Stochastic Processes, New York: Springer-Verlag.
2. Cai, Z., Fan, J., and Li, R. Z. (2000a), "Efficient Estimation and Inferences for Varying-Coefficient Models," Journal of the American Statistical Association, 95, 888-902.
3. Cai, Z., Fan, J., and Yao, Q. (2000b), "Functional-Coefficient Regression Models for Nonlinear Times Series," Journal of the American Statistical Association, 95, 941-956.
4. Chen, R., and Liu, L. M. (2001), "Functional Coefficient Autoregressive Models: Estimation and Tests of Hypotheses," Journal of Time Series Analysis, 22, 151-173.
5. Chen, R., and Tsay, R. S. (1993a), "Nonlinear Additive ARX Models," Journal of the American Statistical Association, 88, 955-967.
6. _ (1993b), "Functional-Coefficient Autoregressive Models," Journal of the American Statistical Association, 88, 298-308.
7. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall.
8. Fan, J., Härdle, W., and Mammen, E. (1998), "Direct Estimation of Low-Dimensional Components in Additive Models," The Annals of Statistics, 26, 943-971.
9. Franses, H. F. (1996), Periodicity and Stochastic Trends in Economic Time Series, Oxford, U.K.: Oxford University Press.
10. Härdle, W., Hlavka, Z., and Klinke, S. (2000), XploRe Application Guide, Heidelberg: Springer-Verlag.
11. Hardie, W., Liang, H., and Gao, J. T. (2000), Partially Linear Models, Heidelberg: Springer-Verlag.
12. Härdle, W., and Mammen, E. (1993), "Comparing Nonparametric versus Parametric Regression Fits," The Annals of Statistics, 21, 1926-1947.
13. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman & Hall.
14. _ (1993), "Varying-Coefficient Models," Journal of the Royal Statistical Society, Ser. B, 55, 757-796.
15. Hjellvik, V., Yao, Q., and Tjøstheim, D. (1998), "Linearity Testing Using Local Polynomial Approximation," Journal of Statistical Planning and Inference, 68, 295-321.
16. Katkovnik, V. Ya. (1979), "Linear and Nonlinear Methods of Nonparametric Regression Analysis," Soviet Automatic Control, 93, 35-46 [Russian].
17. Linton, O. B. (1997), "Efficient Estimation of Additive Nonparametric Regression Models," Biometrika, 84, 469-473.
18. Linton, O. B., and Härdle, W. (1996), "Estimation of Additive Regression Models With Known Links," Biometrika, 83, 529-540.
19. Linton, O. B., and Nielsen, J. P. (1995), "A Kernel Method of Estimating Structured Nonparametric Regression Based on Marginal Integration," Biometrika, 82, 93-100.
20. Liptser, R. Sh., and Shirjaev, A. N. (1980), "A Functional Central Limit Theorem for Martingales," Theory of Probability and Applications, 25, 667-688.
21. Liu, R. (1988), "Bootstrap Procedures Under Some Non I.I.D. Models," The Annals of Statistics, 16, 1696-1708.
22. Mammen, E. (1992), When Does Bootstrap Work: Asymptotic Results and Simulations, Berlin: Springer-Verlag.
23. Mammen, E., Linton, O., and Nielsen, J. (1999), "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," The Annals of Statistics, 5, 1443-1490.
24. Masry, E., and Tjøstheim, D. (1995), "Non-Parametric Estimation and Identification of ARCH Nonlinear Time Series: Strong Convergence and Asymptotic Normality," Econometric Theory, 11, 258-289.
25. _ (1997), "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, 13, 214-252.
26. Ruppert, D., Sheather, S. J., and Wand, M. P. (1995), "An Effective Bandwidth Selection for Local Least Squares Regression," Journal of the American Statistical Association, 90, 1257-1270.
27. Ruppert, D., and Wand, M. P. (1994), "Multivariate Locally Weighted Least Squares Regression," The Annals of Statistics, 22, 1346-1370.
28. Sperlich, S., Tjøstheim, D., and Yang, L. (2002), "Nonparametric Estimation and Testing of Interaction in Additive Models," Econometric Theory, 18, 197-251.
29. Stone, C. J. (1977), "Consistent Nonparametric Regression," The Annals of Statistics, 5, 595-645.
30. Tjøstheim, D., and Auestad, B. (1994), "Nonparametric Identification of Nonlinear Time Series: Projections," Journal of the American Statistical Association, 89, 1398-1409.
31. Wand, M. P., and Jones, M. C. (1995), Kernel Smoothing, London: Chapman & Hall.
32. Wolters, J. (1992), "Persistence and Seasonality in Output and Employment of the Federal Republic of Germany," Recherches Economiques de Louvain, 58, 421-439.
33. Wu, C. F. J. (1986), "Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis" (with discussion), The Annals of Statistics, 14, 1261-1350.
34. Yang, L., and Tschernig, R. (2002), "Non- and Semiparametric Identification of Seasonal Nonlinear Autoregression Models," Econometric Theory, 18, 1408-1448.
35. Yoshihara, K. (1976), "Limiting Behavior of U-Statistics for Stationary, Absolutely Regular Processes," Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 35, 237-252.