On the use of the bootstrap for estimating functions with functional data

Computational Statistics and Data Analysis

Volumn 51, Issue 2, 2006, Pages 1063-1074

  Cuevas, Antonio ^a   Febrero, Manuel ^b   Fraiman, Ricardo ^c  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^c UNIVERSIDAD DE SAN ANDRÉS   (Argentina)

Author keywords

Bootstrap; Bootstrap validity; Functional data; Functional median; Smoothed bootstrap; Trimmed functional mean

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; MONTE CARLO METHODS; PARAMETER ESTIMATION;

BOOTSTRAP; BOOTSTRAP VALIDITY; FUNCTIONAL DATA; FUNCTIONAL MEDIAN; SMOOTHED BOOTSTRAP; TRIMMED FUNCTIONAL MEAN;

FUNCTION EVALUATION;

EID: 33750282724     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2005.10.012     Document Type: Article

References (30)

1. Bickel P.J., and Freedman D.A. Some asymptotic theory for the bootstrap. Ann. Statist. 9 (1981) 1196-1217
2. Bickel P.J., Klaassen C., Ritov Y., and Wellner J.A. Efficient and Adaptive Estimation for Semiparametric Models (1993), Johns Hopkins University Press, Baltimore
3. Boente G., and Fraiman R. Kernel-based functional principal components. Statist. Probab. Lett. 48 (2000) 335-345
4. Cardot H., and Sarda P. Estimation in generalized linear models for functional data via penalized likelihood. J. Multivariate Anal. 92 (2005) 24-41
5. Cardot H., Ferraty F., Mas A., and Sarda P. Testing hypotheses in the functional linear model. Scand. J. Statist. 30 (2003) 241-255
6. Cuevas A., and Fraiman R. On the bootstrap methodology for functional data. In: Antoch J. (Ed). Proceedings in Computational Statistics, COMPSTAT 2004 (2004), Physica-Verlag, Heidelberg 127-135
7. Cuevas A., Febrero M., and Fraiman R. Cluster analysis: a further approach based on density estimation. Comput. Statist. Data Anal. 36 (2001) 441-459
8. Cuevas A., Febrero M., and Fraiman R. An anova test for functional data. Comput. Statist. Data Anal. 47 (2004) 111-122
9. Dimitriadou, E., Hornik, K., Leisch, F., Meyer, D., Weingessel, A., 2004. e1071: Misc Functions of the Department of Statistics, TU Wien. R package version 1.5-1. http://www.R-project.org.
10. Dudley R.M. Nonlinear functionals of empirical measures and the bootstrap. In: Eberlein E., Kuelbs J., and Marcus M.B. (Eds). Probability in Banach Spaces, vol. 7 (Oberwolfach, 1988) (1990), Birkhäuser, Boston 63-82
11. Ferraty F., and Vieu P. The functional nonparametric model and application to spectrometric data. Comput. Statist. 17 (2002) 545-564
12. Fraiman R., and Muniz G. Trimmed means for functional data. Test 10 (2001) 419-440
13. Gasser T., Hall P., and Presnell B. Nonparametric estimation of the mode of a distribution of random curves. J. Roy. Statist. Soc. B 60 (1998) 681-691
14. Gill R.D. Non- and semi-parametric maximum likelihood estimators and the von Mises method. I. Scand. J. Statist. 16 (1989) 97-128
15. Giné E., and Zinn J. Bootstrapping general empirical measures. Ann. Probab. 18 (1990) 851-869
16. Hall P. Theoretical comparison of bootstrap confidence intervals (with discussion). Ann. Statist. 16 (1988) 927-985
17. Hall P., and Heckman N. Estimating and depicting the structure of a distribution of random functions. Biometrika 89 (2002) 145-158
18. Laha L.G., and Rohatgi V.K. Probability Theory (1979), Wiley, New York
19. Parr W.C. The bootstrap: some large sample theory and connections with robustness. Statist. Probab. Lett. 3 (1985) 97-100
20. Politis D.N., and Romano J.P. Limit theorems for weakly dependent Hilbert space valued random variables with application to the stationary bootstrap. Statist. Sin. 4 (1994) 461-476
21. R Development Core Team., 2004. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org.
22. Ramsay J.O., and Silverman B.W. Functional Data Analysis (1997), Springer, New York
23. Ramsay J.O., and Silverman B.W. Applied Functional Data Analysis (2002), Springer, New York
24. Rice J.A. Functional and longitudinal data analysis: perspectives on smoothing. Statist. Sin. 14 (2004) 631-647
25. Ruiz-Meana M., García-Dorado D., Pina P., Inserte J., Agulló L., and Soler-Soler J. Cariporide preserves mitochondrial proton gradient and delays ATP depletion in cardiomyocites during ischemic conditions. Amer. J. Physiol. Heart Circulatory Physiol. 285 (2003) H999-H1006
26. Sheehy A., and Wellner J.A. Uniform Donsker classes of functions. Ann. Probab. 20 (1992) 1983-2030
27. van der Vaart A., and Wellner J. Weak Convergence and Empirical Processes (1996), Springer, New York
28. Venables W.N., and Ripley B.D. Modern Applied Statistics with S. fourth ed (2002), Springer, New York
29. Yukich J.E. Uniform exponential bounds for the normalized empirical process. Stud. Math. 84 (1986) 71-78
30. Yurinskii V.V. Exponential inequalities for sums of random vectors. J. Multivariate Anal. 6 (1976) 473-479