Simultaneous confidence bands for nonparametric regression with functional data

Statistica Sinica

Volumn 21, Issue 4, 2011, Pages 1735-1765

  Degras, David A ^a  

^a DEPAUL UNIVERSITY   (United States)

Author keywords

Functional asymptotic normality; Functional data; Goodnessof fit test; Nonparametric regression; Simultaneous confidence bands

Indexed keywords

EID: 84857141061     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2009.207     Document Type: Article

References (30)

1. Adler, R. J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. IMS, Hayward, CA.
2. Azzalini, A. and Bowman, A. (1993). On the use of nonparametric regression for checking linear relationships. J. Roy. Statist. Soc. Ser. B 55, 549-557.
3. Baraud, Y. (2004). Confidence balls in Gaussian regression. Ann. Statist. 32, 528-551. (Pubitemid 41250304)
4. Butler, R. and Paolella, M. (2002). Calculating the density and distribution function for the singly and doubly noncentral F. Statist. Comput. 12, 9-16. (Pubitemid 37132833)
5. Degras, D. (2008). Asymptotics for the nonparametric estimation of the mean function of a random process. Statist. Probab. Lett. 78, 2976-2980.
6. Degras, D. (2009). Nonparametric estimation of a trend based upon sampled continuous processes. C. R. Acad. Sci. Paris, Ser. I 347, 191-194.
7. Deheuvels, P. and Mason, D. (2004). General asymptotic condence bands based on kernel-type function estimators. Statist. Infer. Stochast. Proc. 7, 225-277. (Pubitemid 39604979)
8. Eubank, R. L. and Speckman, P. L. (1993). Confidence bands in nonparametric regression. J. Amer. Statist. Assoc. 88, 1287-1301.
9. Fan, J. (1992). Design-adaptive nonparametric regression. J. Amer. Statist. Assoc. 87, 998-1004.
10. Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis. Theory and practice. Springer, New York.
11. Geman, S. (1980). A limit theorem for the norm of random matrices. Ann. Probab. 8, 252-261.
12. Hall, P. and Titterington, D. M. (1988). On confidence bands in nonparametric density estimation and regression. J. Multivariate Anal. 27, 228-254.
13. Härdle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21, 1926-1947.
14. Hart, J. D. and Wehrly, T. E. (1986). Kernel regression estimation using repeated measurements data. J. Amer. Statist. Assoc. 81, 1080-1088.
15. Hart, J. D. and Wehrly, T. E. (1993). Consistency of cross-validation when the data are curves. Stoch. Proces. Applic. 45, 351-361.
16. Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd edition. Springer, New York.
17. Johansen, S. and Johnstone, I. M. (1990). Hotelling's theorem on the volume of tubes: some illustrations in simultaneous inference and data analysis. Ann. Statist. 18, 652-684.
18. Landau, H. and Shepp, L. A. (1970). On the supremum of a Gaussian process. Sankhyā 32, 369-378.
19. Neumann, M. H. and Polzehl, J. (1998). Simultaneous bootstrap confidence bands in nonparametric regression. J. Nonparam. Statist. 9, 307-333. (Pubitemid 128547518)
20. Pollard, D. (1990). Empirical Processes: Theory and Applications. Institute of Mathematical Statistics, Hayward, CA.
21. Ramsay, J. O., and Silverman, B. W. (2005). Functional Data Analysis. 2nd edition. Springer, New York.
22. Robinson, P. M. (1997). Large-sample inference for nonparametric regression with dependent errors. Ann. Statist. 25, 2054-2083.
23. Song, P. X.-K., Gao, X., Liu, R. and Le, W. (2006). Nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome. Biometrics 62, 545-554. (Pubitemid 43926660)
24. Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist. 25, 613-641.
25. Sun, J. and Loader, C. (1994). Simultaneous confidence bands for linear regression and smoothing. Ann. Statist. 22, 1328-1347.
26. Wang, J. (2009). Modelling time trend via spline confidence band. Submitted. Available at http://www.math.uic.edu/~wangjing/
27. Wang, J. and Yang, L. (2009). Polynomial spline confidence bands for regression curves. Statist. Sinica 19, 325-342.
28. Wu, W. B. and Zhao, Z. (2007). Inference of trends in time series. J. Roy. Statist. Soc. Ser. B 69, 391-410.
29. Yao, F. (2007). Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data. J. Multivariate Anal. 98, 40-56. (Pubitemid 44567405)
30. Zhao, Z. and Wu, W. B. (2008). Confidence bands in nonparametric time series regression. Ann. Statist. 36, 1854-1878.