Cross-validation approximation in functional linear regression

Journal of Statistical Computation and Simulation

Volumn 83, Issue 8, 2013, Pages 1429-1439

  Hosseini Nasab, Mohammad ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

cross validation; eigenfunction; eigenvalue; functional data analysis; regression; stochastic expansion

Indexed keywords

EID: 84882582742     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2012.662502     Document Type: Article

References (20)

1. Amatoa, U., Antoniadisb, A. and De Feisa, I. 2006. Dimension reduction in functional regression with applications. Comput. Statist. Data Anal, 50: 2422 - 2446. (doi:10.1016/j.csda.2004.12.007)
2. Ramsay, J. O. and Silverman, B. W. 2002. Applied Functional Data Analysis, New York: Springer.
3. Ramsay, J. O. and Silverman, B. W. 2005. Functional Data Analysis, 2, New York: Springer.
4. Yao, F., Muller, H. G. and Wang, G. L. 2005. Functional linear regression analysis for longitudinal data. Ann. Stat, 33 (6): 2873 - 2903. (doi:10.1214/009053605000000660)
5. Viviani, R., Gron, G. and Spitzer, M. 2005. Functional principal component analysis of fMRI data. Human Brain Mapping, 24: 109 - 129. (doi:10.1002/hbm.20074)
6. Nerinia, D. and Ghattas, B. 2007. Classifying densities using functional regression trees: Applications in oceanology. Comput. Stat. Data Anal, 51: 4984 - 4993. (doi:10.1016/j.csda.2006.09.028)
7. Matsui, H., Araki, Y. and Konishi, S. 2008. Multivariate regression modeling for functional data. J. Data Sci, 6: 313 - 331.
8. Shin, H. 2009. Partial functional linear regression. J. Stat. Plann. Infer, 139: 3405 - 3418. (doi:10.1016/j.jspi.2009.03.001)
9. He, G., Muller, H. G. and Wang, J-L. 2010. Functional linear regression via canonical analysis. Bernoulli, 16 (3): 705 - 729. (doi:10.3150/09-BEJ228)
10. He, G., Müller, H. G., Wang, J. L. and Yang, W. 2010. Functional linear regression via canonical analysis. Bernoulli, 16 (3): 707 - 729.
11. Hall, P. and Hosseini-Nasab, M. 2006. On properties of functional principal components analysis. J. R. Stat. Soc. B: Stat. Methodol, 68: 109 - 126. (doi:10.1111/j.1467-9868.2005.00535.x)
12. Cai, T. and Hall, P. 2007. Prediction in functional linear regression. Ann. Statist, 34: 2159 - 2179. (doi:10.1214/009053606000000830)
13. Hall, P. and Hosseini-Nasab, M. 2009. Theory for high-order bounds in functional principal components analysis. Math. Proc. Camb. Phil. Soc, 149: 225 - 56. (doi:10.1017/S0305004108001850)
14. Ferraty, F. and Vieu, P. 2000. Fractal dimensionality and regression estimation in semi-normed vectorial spaces. C.R. Acad. Sci. Paris Ser. I, 330: 139 - 142.
15. Cuevas, A., Febrero, M. and Fraiman, R. 2002. Linear functional regression: The case of fixed design and functional response. Can. J. Statist, 30: 285 - 300. (doi:10.2307/3315952)
16. Cardot, H., Ferraty, F. and Sarda, P. 2003. Spline estimators for the functional linear model. Statist. Sin, 13: 571 - 591.
17. Li, Y. and Hsing, T. 2007. On rates of convergence in functional linear regression. J. Multivariate Anal, 98 (9): 1782 - 1804. (doi:10.1016/j.jmva.2006.10.004)
18. Hall, P. and Horowitz, J. L. 2007. Methodology and convergence rates for functional linear regression. Ann. Statist, 35: 70 - 91. (doi:10.1214/009053606000000957)
19. Park, B. U. and Marron, J. S. 1990. Comparison of data-driven bandwidth selectors. J. Am. Statist. Assoc, 85: 66 - 72. (doi:10.1080/01621459.1990.10475307)
20. Hall, P. and Marron, J. S. 1991. Local minima in cross-validation functions. J. R. Statist. Soc. B, 53: 245 - 252.