Spline confidence bands for functional derivatives

Journal of Statistical Planning and Inference

Volumn 142, Issue 6, 2012, Pages 1557-1570

  Cao, Guanqun ^a   Wang, Jing ^b   Wang, Li ^c   Todem, David ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^c UNIVERSITY OF GEORGIA   (United States)

Author keywords

B spline; Eigenfunctions; Functional data; Karhunen Lo ve representation; Semiparametric efficiency

Indexed keywords

EID: 84862806437     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2012.01.009     Document Type: Article

References (35)

1. Cao, G., Wang, L., Li, Y., Yang, L., 2011. Spline confidence envelopes for covariance function in dense functional/longitudinal data. Manuscript.
2. Cao, G., Yang, L., Todem, D. Simultaneous inference for the mean function of dense functional data. Journal of Nonparametric Statistics, forthcoming.
3. Claeskens G., Van Keilegom I. Bootstrap confidence bands for regression curves and their derivatives. Annals of Statistics 2003, 31:1852-1884.
4. Cso{doubleacute}rgo{doubleacute} M., Révész P. Strong Approximations in Probability and Statistics 1981, Academic Press, New York, London.
5. de Boor C. A Practical Guide to Splines 2001, Springer-Verlag, New York.
6. Degras D.A. Simultaneous confidence bands for nonparametric regression with functional data. Statistica Sinica 2011, 21:1735-1765.
7. DeVore R., Lorentz G. Constructive Approximation: Polynomials and Splines Approximation 1993, Springer-Verlag, Berlin.
8. Fan J., Gijbels I. Local Polynomial Modelling and its Applications 1996, Chapman and Hall, London.
9. Ferraty F., Vieu P. Nonparametric Functional Data Analysis: Theory and Practice 1996, Springer, New York.
10. Gasser T., Müller H.G. Estimating regression functions and their derivatives by the kernel method. Scandinavian Journal of Statistics 1984, 11:171-185.
11. Hall P., Hosseini-Nasab M. On properties of functional principal components analysis. Journal of the Royal Statistical Society: Series B 2006, 68:109-126.
12. Hall P., Müller H.G., Wang J.L. Properties of principal component methods for functional and longitudinal data analysis. Annals of Statistics 2006, 34:1493-1517.
13. Hall P., Müller H.G., Yao F. Estimation of functional derivatives. Annals of Statistics 2009, 37:3307-3329.
14. Härdle W. Asymptotic maximal deviation of M-smoothers. Journal of Multivariate Analysis 1989, 29:163-179.
15. Huang J. Local asymptotics for polynomial spline regression. Annals of Statistics 2003, 31:1600-1635.
16. Li Y., Hsing T. Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data. Annals of Statistics 2010, 38:3321-3351.
17. Liu B., Müller H.G. Estimating derivatives for samples of sparsely observed functions, with application to online auction dynamics. Journal of the American Statistical Association 2009, 104:704-717.
18. Ma S., Yang L., Carroll R.J. A simultaneous confidence band for sparse longitudinal regression. Statistica Sinica 2012, 22:95-122.
19. Morris J.S., Carroll R.J. Wavelet-based functional mixed models. Journal of the Royal Statistical Society, Series B 2006, 68:179-199.
20. Müller H.G. Functional modeling of longitudinal data. Longitudinal Data Analysis (Handbooks of Modern Statistical Methods) 2009, 223-252. Wiley, New York. G. Fitzmaurice, M. Davidian, G. Verbeke, G. Molenberghs (Eds.).
21. Ramsay J.O., Silverman B.W. Functional Data Analysis 2005, Springer, New York.
22. Rice J.A., Wu C.O. Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 2001, 57:253-259.
23. Schumaker L. Spline Functions Basic Theory 2007, Cambridge University Press, Cambridge. Third ed.
24. Shi M., Weiss R.E., Taylor J.M.G. An analysis of paediatric CD4 counts for acquired immune deficiency syndrome using flexible random curves. Journal of the Royal Statistical Society, Series B 1996, 45:151-163.
25. Stone C.J. The use of polynomial splines and their tensor products in multivariate function estimation. Annals of Statistics 1994, 22:118-184.
26. Wahba G. Spline Models for Observational Data 1990, vol. 59. SIAM, Philadelphia, PA.
27. Wang J., Yang L. Polynomial spline confidence bands for regression curves. Statistica Sinica 2009, 19:325-342.
28. Wang L., Yang L. Spline estimation of single index model. Statistica Sinica 2009, 19:765-783.
29. Xia Y. Bias-corrected confidence bands in nonparametric regression. Journal of the Royal Statistical Society, Series B 1998, 60:797-811.
30. Yao F., Lee T.C.M. Penalized spline models for functional principal component analysis. Journal of the Royal Statistical Society, Series B 2006, 68:3-25.
31. Yao F., Müller H.G., Wang J.L. Functional linear regression analysis for longitudinal data. Annals of Statistics 2005, 33:2873-2903.
32. Yao F., Müller H.G., Wang J.L. Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 2005, 100:577-590.
33. Zhou L., Huang J., Carroll R.J. Joint modelling of paired sparse functional data using principal components. Biometrika 2008, 95:601-619.
34. Zhou S., Shen X., Wolfe D.A. Local asymptotics of regression splines and confidence regions. Annals of Statistics 1998, 26:1760-1782.
35. Zhou S., Wolfe D.A. On derivative estimation in spline regression. Statistica Sinica 2000, 10:93-108.