Nonparametric Regression with Correlated Errors

Statistical Science

Volumn 16, Issue 2, 2001, Pages 134-153

  Opsomer, Jean ^a   Wang, Yuedong ^b   Yang, Yuhong ^b  

^a Snedecor Hall ^*  (United States)

^b NONE

Author keywords

Adaptive estimation; Kernel regression; Smoothing parameter selection; Splines; Wavelet regression

Indexed keywords

EID: 0009955854     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1009213287     Document Type: Article

References (56)

1. ADENSTEDT, R. K. (1974). On large sample estimation for the mean of a stationary sequence. Ann. Statist. 2 1095-1107.
2. ALTMAN, N. (1994). Krige, smooth, both or neither? Technical report, Biometrics Unit, Cornell Univ.
3. ALTMAN, N. S. (1990). Kernel smoothing of data with correlated errors. J. Amer. Statist. Assoc. 85 749-759.
4. ARONSZAJN, N. (1950). Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 337-404.
5. BARRON, A. R. and BARRON, R. L. (1988). Statistical learning networks: a unifying view. In Computer Science and Statistics: Proceedings of the 21st Interface, 192-203.
6. BERAN, J. (1992). Statistical methods for data with long-range dependence. Statist. Sci. 7 404-416.
7. BERAN, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York.
8. BIERENS, H. (1983). Uniform consistency of kernel estimators of a regression function under generalized conditions. J. Amer. Statist. Assoc. 78 699-707.
9. BREIMAN, L., FRIEDMAN, J. H., OLSHEN, R. and STONE, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
10. CHIU, S.-T. (1989). Bandwidth selection for kernel estimate with correlated noise. Statist. Probab. Lett. 8 347-354.
11. CHU, C.-K. and MARRON, J. S. (1991). Comparison of two bandwidth selectors with dependent errors. Ann. Statist. 19 1906-1918.
12. COLLOMB, G. and HÄRDLE, W. (1986). Strong uniform convergence rates in robust nonparametric time series analysis. Stochastic Process. Appl. 23 77-89.
13. Cox, D. R. (1984). Long-range dependence: a review. In Statistics: An Appraisal. Proceedings 50th Anniversary Conference, (H. A. David and H. T. David, eds.) 55-74. Iowa State Univ. Press.
14. DIGGLE, P. J. and HUTCHINSON, M. F. (1989). On spline smoothing with autocorrelated errors. Austral. J. Statist. 31 166-182.
15. DONOHO, D. L. and JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26 879-921.
16. EFROMOVICH, S. (1999). How to overcome curse of long-memory errors in nonparametric regression. IEEE Trans. Inform. Theory 45, 1735-1741.
17. FRIEDMAN, J. and STUETZLE, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76 817-823.
18. GU, C. and WAHBA, G. (1993). Semiparametric ANOVA with tensor product thin plate spline. J. Roy. Statist. Assoc. Ser. B 55 353-368.
19. HALL, P. and HART, J. D. (1990). Nonparametric regression with long-range dependence. Stochastic Process. Appl. 36 339-351.
20. HALL, P. Lahiri, S. N. and POLZEHL, J. (1995). On bandwidth choice in nonparametric regression with both short- and long-range dependent errors. Ann. Statist. 23 1921-1936.
21. HARDLE, W., HALL, P. and MARRON, J. S. (1988). How far are automatically chosen regression smoothing parameters from their optimum? J. Amer. Statist. Assoc. 83 86-95.
22. HARDLE, W., HALL, P. and MARRON, J. S. (1992). Regression smoothing parameters that are not far from their optimum. J. Amer. Statist. Assoc. 87 227-233.
23. HART, D. (1997). Nonparametric Smoothing and Lack-of-Fit Tests. Springer, New York.
24. HART, J. D. (1991). Kernel regression estimation with time series errors. J. Roy. Statist. Assoc. Ser. B 53 173-187.
25. HART, J. D. (1994). Automated kernel smoothing of dependent data by using time series cross-validation. J. Roy. Statist. Assoc. Ser. B 56 529-542.
26. HARVILLE, D. (1976). Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann. Statist. 4 384-395.
27. HERRMANN, E., GASSER, T. and KNEIP, A. (1992). Choice of bandwidth for kernel regression when residuals are correlated. Biometrika 79 783-795.
28. JOHNSTONE, I. and SILVERMAN, B. (1997). Wavelet threshold estimators for data with correlated noise. J. Roy. Statist. Assoc. Ser. B 59 319-351.
29. KIMELDORF, G. S. and WAHBA, G. (1971). Some results on Tchebycheffian spline functions. J. Math. Anal. Appl. 33 82-94.
30. KOHN, R., ANSLEY, C. F. and THARM, D. (1991). The performance of cross-validation and maximum likelihood estimators of spline smoothing parameters. J. Amer. Statist. Assoc. 86 1042-1050.
31. KOHN, R., ANSLEY, C. F. and WONG, C. (1992). Nonparametric spline regression with autoregressive moving average errors. Biometrika 79 335-346.
32. KÜNSCH, H., BERAN, J. and HAMPEL, F. (1993). Contrasts under long-range correlations. Ann. Statist. 21 943-964.
33. LASLETT, G. (1994). Kriging and splines: an empirical comparison of their predictive performance in some applications. J. Amer. Statist. Assoc. 89 392-409.
34. NASON, G. P. (1996). Wavelet shrinkage using cross-validation. J. Roy. Statist. Soc. Ser. B 58 463-479.
35. NICOLERIS, T. and YATRACOS, Y. G. (1997). Rate of convergence of estimates, Kolmogrov's entropy and the dimensionality reduction principle in regression. Ann. Statist. 25 2493-2511.
36. OPSOMER, J.-D. (1995). Estimating a function by local linear regression when the errors are correlated. Preprint 95-42, Dept. Statistics, Iowa State Univ.
37. OPSOMER, J.-D. (1997). Nonparametric regression in the presence of correlated errors. In Modelling Longitudinal and Spatially Correlated Data: Methods, Applications and Future Directions (T. Gregoire, D. Brillinger, P. Diggle, E. Russek-Cohen, W. Warren and R. Wolfinger, eds.) 339-348. Springer, New York.
38. OPSOMER, J.-D. and RUPPERT, D. (1997). Fitting a bivariate additive model by local polynomial regression. Ann. Statist. 25 186-211.
39. OPSOMER, J.-D. and RUPPERT, D. (1998). A fully automated bandwidth selection method for fitting additive models by local polynomial regression. J. Amer. Statist. Assoc. 93 605-619.
40. PRIESTLEY, M. B. and CHAO, M. T. (1972). Nonparametric function fitting. J. Roy. Statist. Assoc. Ser. B 34 385-392.
41. RUPPERT, D., SHEATHER, S. J. and WAND, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90 1257-1270.
42. RUPPERT, D. and WAND, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22 1346-1370.
43. STONE, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22 118-184.
44. STONE, C. J. HANSEN, M. H. KOOPERBERG, C. and TRUONG, Y. (1997). Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann. Statist. 25 1371-1470.
45. WAHBA, G. (1978). Improper priors, spline smoothing, and the problem of guarding against model errors in regression. J. Roy. Statist. Assoc. Ser. B 40 364-372.
46. WAHBA, G. (1983). Bayesian confidence intervals for the cross-validated smoothing spline. J. Roy. Statist. Assoc. Ser. B 45 133-150.
47. WAHBA, G. (1985). A comparison of GCV and GML for choosing the smoothing parameters in the generalized spline smoothing problem. Ann. Statist. 4 1378-1402.
48. WAHBA, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
49. WAHBA, G. and WANG, Y. (1993). Behavior near zero of the distribution of GCV smoothing parameter estimates for splines. Statist. Probab. Lett. 25 105-111.
50. WAHBA, G. WANG, Y., Gu, C., KLEIN, R. and KLEIN, B. (1995). Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy. Ann. Statist. 23 1865-1895.
51. WANG, Y. (1996). Function estimation via wavelet shrinkage for long-memory data. Ann. Statist. 24 466-484.
52. WANG, Y. (1998a). Mixed-effects smoothing spline ANOVA. J. Roy. Statist. Assoc. Ser. B 60 159-174.
53. WANG, Y. (1998b). Smoothing spline models with correlated random errors. J. Amer. Statist. Assoc. 93 341-348.
54. YANG, Y. (1997). Nonparametric regression with dependent errors. Preprint 97-29, Dept. Statistics, Iowa State Univ. (A shorter version is accepted in Bernoulli.)
55. YANG, Y. (1999). Model selection for nonparametric regression. Statist. Sinica 9 475-499.
56. YANG, Y. (2000). Combining different procedures for adaptive regression. J. Multivariate Anal. 74 135-161.