Local polynomial regression estimation with correlated errors

Communications in Statistics - Theory and Methods

Volumn 30, Issue 7, 2001, Pages 1271-1293

  Francisco Fernandez M ^a   Vilar Fernandez J M ^a  

^a UNIVERSITY OF A CORUÑA   (Spain)

Author keywords

Autoregressive process; Local polynomial Fitting; Nonparametric estimators

Indexed keywords

EID: 0034885608     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-100104745     Document Type: Article

References (32)

1. Lejeune, M. Estimation non-paramétrique par noyaux: régression polynomiale mobile. Revue de Statist. Appliq. 1985, 33, 43-68.
2. Müller, H.G. Nonparametric regression analysis of longitudinal data; Notes in Statistics, Springer: Berlin, 1988; Vol 46.
3. Tsybakov, A.B. Robust reconstruction of functions by the local-approximation method. Problems of Information Transmission 1986, 22, 133-146.
4. Fan, J. Design-adaptive nonparametric regression. J. Am. Stat. Assoc. 1992, 87, 998-1004.
5. Fan, J. Local linear regression smoothers and their minimax efficiency. Ann. Stat. 1993, 21, 196-216.
6. Hastie, T.; Loader, C. Local regression: automatic kernel carpentry. Stat. Science 1993, 8 (2), 120-143.
7. Fan, J.; Gijbels, I. Variable bandwidth and local linear regression smoothers. Ann. Stat. 1992, 20, 2008-2036.
8. Fan, J.; Gijbels, I. Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J. Roy. Stat. Soc. B 1995, 57 (2), 371-394.
9. Ruppert, D.; Wand, P. Multivariate locally weighted least squares regression. Ann. Stat. 1994, 22, 1346-1370.
10. Fan, J.; Gasser, T.; Gijbels, I.; Brockmann, M.; Engel, J. Local polynomial regression: optimal kernels and asymptotic minimax efficiency. Ann. Inst. Stat. Math. 1997, 49 (1), 79-99.
11. Masry, E.; Fan, J. Local polynomial estimation of regression function for mixing processes. Scand. J. of Stat. 1997, 24, 165-179.
12. Masry, E. Multivariate regression estimation: local polynomial fitting for time series. Stoch. Proc. Appl. 1996a, 65, 81-101.
13. Masry, E. Multivariate local polynomial regression for time series: uniform strong consistency and rates. J. Time Ser. Anal. 1996b, 17, 571-599.
14. Hardle, W.; Tsybakov, A. Local polynomial estimators of the volatility function in nonparametric autoregression. J. of Econometrics 1997, 81, 223-242.
15. Hardle, W.; Tsybakov, A.; Yang L. Nonparametric vector autoregression. J. of Statistical Planning and Inference 1998, 68, 221-245.
16. Opsomer, J.D. Nonparametric regression in the presence of correlated errors. In Modelling Longitudinal and Spatially Correlated Data: Methods, Applications and Future Directions; Gregoire, T.G., Brillinger, D.R., Diggle, P.J., Russek-Cohen, E., Warren, W.G., Wolfinger, R.D., Eds.; Springer: New York, 1997, 339-348.
17. Vilar-Fernández, J.A.; Vilar-Fernández, J.M. Recursive estimation of regression functions by local polynomial fitting. Ann. Ins. Stat. Math. 1998, 50 (4), 729-754.
18. Vilar-Fernández, J.M.; Vilar-Fernández, J.A. Recursive local polynomial regression under dependence conditions. TEST 2000, 9 (1), 209-233.
19. Fan, J.; Gijbels, I. Local polynomial modelling and its applications; Chapman and Hall: London, 1996.
20. Hart, J. Kernel regression estimation with time series errors. J.R. Statist. Soc. B 1991, 53, 173-187.
21. Chu, C.K.; Marron, J.S. Comparison of two bandwidth selectors with dependent errors. The Annals of Statistics 1991, 19 (4), 1906-1918.
22. Tran, L.; Roussas, G.; Yakowitz, S.; Truong, V. Fixed-design regression for linear time series. Ann. Stat. 1996, 24 (3), 975-991.
23. Rosenblatt, M. A central limit theorem and strong mixing conditions. Proc. Nat. Acad. Sci. 1956, 4, 43-47.
24. Doukhan, P. Mixing. Properties and examples; Notes in Statistics, Springer: Berlin, 1995; Vol 85.
25. Hardle, W.; Vieu, P. Kernel regression smoothing of time series. J. Time Ser. Anal. 1992, 13, 209-232.
26. Hart, J. Automated kernel smoothing of dependent data by using time series cross-validation. J.R. Statist. Soc. B 1994, 56 (3), 529-542.
27. Herrmann, E.; Gasser, T.; Kneip, A. Choice of bandwidth for kernel regression when residuals are correlated. Biometrika 1992, 79 (4), 783-795.
28. Quintela, A. A plug-in technique in nonparametric regression with dependence. Comm. In Statist., Theory and Methods 1994, 23 (9), 2581-2605.
29. Müller, H.G.; Stadtmüller, U. Detecting dependencies in smooth regression models. Biometrika 1988, 75 (4), 639-650.
30. Fan, J.; Gijbels, I.; Hu, T.C.; Huang, L.S. A study of variable bandwidth selection for local polynomial regression. Statistica Sinica 1996, 6, 113-127.
31. Volkonskii, V.A.; Rozanov, Yu. A. Some limit theorems for random functions. Theory Prob. Appl. 1959, 4, 178-197.
32. Cleveland, W.S.; Devlin, S.J. Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 1988, 83, 597-610.