Continuously additive models for nonlinear functional regression

Biometrika

Volumn 100, Issue 3, 2013, Pages 607-622

  Müller, Hans Georg ^a   Wu, Yichao ^b   Yao, Fang ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Berkeley growth study; Functional data analysis; Functional regression; Gene expression; Generalized response; Stochastic process; Tensor spline

Indexed keywords

EID: 84882730974     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/ast004     Document Type: Article

References (30)

1. Cai, T. & hall, P. (2006). Prediction in functional linear regression. Ann. Statist. 34, 2159-79
2. Cardot, H., Crambes, C., Kneip, A.&SARDA, P. (2007). Smoothing splines estimators in functional linear regression with errors-in-variables. Comp. Statist. Data Anal. 51, 4832-48 (Pubitemid 46635889)
3. Cardot, H. & Sarda, P. (2005). Estimation in generalized linear models for functional data via penalized likelihood. J. Mult. Anal. 92, 24-41 (Pubitemid 39407452)
4. Carroll, R., Aity, A., Mammen, E. & Yu, K. (2008). Nonparametric additive regression for repeatedly measured data. Biometrika 36, 383-98
5. Crambes, C., Kneip, A. & Sarda, P. (2009). Smoothing splines estimators for functional linear regression. Ann. Statist. 37, 35-72
6. Escabias, M., Aguilera, A. M. & Valderrama, M. J. (2004). Principal component estimation of functional logistic regression: Discussion of two different approaches. J. Nonparam. Statist. 16, 365-84 (Pubitemid 38705958)
7. Faraway, J. J. (1997). Regression analysis for a functional response. Technometrics 39, 254-61 (Pubitemid 127634023)
8. Ferraty, F. & Vieu, P. (2006). Nonparametric Functional Data Analysis. New York: Springer
9. FRIEDMAN, J. & Stuetzle, W. (1981). Projection pursuit regression. J. Am. Statist. Assoc. 76, 817-23
10. Gasser, T., Müller, H-G., Köhler, W., Molinari, L. & Prader, A. (1984). Nonparametric regression analysis of growth curves. Ann. Statist. 12, 210-29
11. Goutis, C. (1998). Second-derivative functional regression with applications to near infra-red spectroscopy. J. R. Statist. Soc. B 60, 103-14 (Pubitemid 128656495)
12. Hall, P., Müller, H-G. & Yao, F. (2009). Estimation of functional derivatives. Ann. Statist. 37, 3307-29
13. Hall, P., Poskitt, D. S. & Presnell, B. (2001). A functional data-Analytic approach to signal discrimination. Technometrics 43, 1-9 (Pubitemid 32159948)
14. James, G. M. (2002). Generalized linear models with functional predictors. J. R. Statist. Soc. B 64, 411-32
15. Kneip, A. & Gasser, T. (1992). Statistical tools to analyze data representing a sample of curves. Ann. Statist. 20, 1266-305
16. Mammen, E. & Park, B. U. (2005). Bandwidth selection for smooth backfitting in additive models. Ann. Statist. 33, 1260-94 (Pubitemid 41137882)
17. Marx, B. & Eilers, B. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci. 11, 89-121 (Pubitemid 126706128)
18. Mclean, M. W., Hooker, G., Staicu, A. M., Scheipl, F. & Ruppert, D. (2013). Functional generalized additive models. J. Comp. Graph. Statist., To Appear
19. Müller, H-G. & StadtMüller, U. (2005). Generalized functional linear models. Ann. Statist. 33, 774-805 (Pubitemid 41053722)
20. Müller, H-G. & Yao, F. (2008). Functional additive models. J. Am. Statist. Assoc. 103, 1534-44
21. Ramsay, J. O. & Silverman, B. W. (2005). Functional Data Analysis. New York: Springer, 2nd ed.
22. RAVIKUMAR, P., Lafferty, J., Liu, H. & Wasserman, L. (2009). Sparse additive models. J. R. Statist. Soc. B 71, 1009-30
23. Reiss, P. & Ogden, R. (2010). Functional generalized linear models with images as predictors. Biometrics 66, 61-9
24. Song, J., Deng, W., Lee, H. & Kwon, D. (2008). Optimal classification for time-course gene expression data using functional data analysis. Comp. Biol. Chem. 32, 426-32
25. Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., Brown, P. O., Botstein, D.& Futcher, B. (1998). Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molec. Biol. Cell 9, 3273-97 (Pubitemid 28551928)
26. Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705
27. Tuddenham, R. & Snyder, M. (1954). Physical growth of California boys and girls from birth to age 18. Calif. Pub. Child Dev. 1, 183-364
28. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439-47
29. Yao, F. & Müller, H-G. (2010). Functional quadratic regression. Biometrika 97, 49-64
30. Yu, K., Park, B. U. & Mammen, E. (2008). Smooth backfitting in generalized additive models. Ann. Statist. 36, 228-60