Additive modelling of functional gradients

Biometrika

Volumn 97, Issue 4, 2010, Pages 791-805

  Müller, Hans Georg ^a   Yao, Fang ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Derivative; Functional data analysis; Functional regression; Gradient field; Nonparametric differentiation; Principal component

Indexed keywords

EID: 78651315755     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asq056     Document Type: Article

References (28)

1. ASH, R. B. & GARDNER, M. F. (1975). Topics in Stochastic Processes. New York: Academic Press [Harcourt Brace Jovanovich Publishers]. Probability and Mathematical Statistics, Vol. 27.
2. BILLINGSLEY, P. (1995). Probability and Measure. Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons Inc., 3rd ed. A Wiley-Interscience Publication.
3. BOENTE, G. & FRAIMAN, R. (2000). Kernel-based functional principal components. Statist. Prob. Lett. 48, 335-45.
4. CAI, T. & HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 34, 2159-79.
5. 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.
6. CAREY, J. R., LIEDO, P., MÜLLER, H.-G., WANG, J.-L. & CHIOU, J.-M. (1998). Relationship of age patterns of fecundity to mortality, longevity, and lifetime reproduction in a large cohort of Mediterranean fruit fly females. J. Gerontol. A.: Biol. Sci. Med. Sci. 53, 245-51.
7. CASTRO, P. E., LAWTON, W. H. & SYLVESTRE, E. A. (1986). Principal modes of variation for processes with continuous sample curves. Technometrics 28, 329-37.
8. CHIOU, J.-M., MÜLLER, H.-G., WANG, J.-L. & CAREY, J. R. (2003). A functional multiplicative effects model for longitudinal data, with application to reproductive histories of female medflies. Statist. Sinica 13, 1119-33.
9. CUEVAS, A., FEBRERO, M. & FRAIMAN, R. (2002). Linear functional regression: The case of fixed design and functional response. Can. J. Statist. 30, 285-300.
10. FAN, J. & GIJBELS, I. (1996). Local Polynomial Modelling and its Applications. London: Chapman & Hall.
11. FERRATY, F. & VIEU, P. (2006). Nonparametric Functional Data Analysis. New York: Springer.
12. GASSER, T. & MÜLLER, H.-G. (1984). Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist. 11, 171-85.
13. GRISWOLD, C., GOMULKIEWICZ, R. & HECKMAN, N. (2008). Hypothesis testing in comparative and experimental studies of function-valued traits. Evolution 62, 1229-42.
14. HALL, P., MÜLLER, H.-G. & YAO, F. (2009). Estimation of functional derivatives. Ann. Statist. 37, 3307-29.
15. HASTIE, T. & TIBSHIRANI, R. (1986). Generalized additive models (with discussion). Statist. Sci. 1, 297-318.
16. IZEM, R. & KINGSOLVER, J. (2005). Variation in continuous reaction norms: Quantifying directions of biological interest. Am. Naturalist 166, 277-89.
17. KIRKPATRICK, M. & HECKMAN, N. (1989). A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27, 429-50.
18. LI, Y. & HSING, T. (2007). On rates of convergence in functional linear regression. J. Mult. Anal. 98, 1782-804.
19. MÜLLER, H.-G. & YAO, F. (2008). Functional additive models. J. Am. Statist. Assoc. 103, 1534-44.
20. MÜLLER, H.-G. & ZHANG, Y. (2005). Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories. Biometrics 61, 1064-75.
21. RAMSAY, J. O. & DALZELL, C. J. (1991). Some tools for functional data analysis. J. R. Statist. Soc. B 53, 539-72.
22. RAMSAY, J. O. & SILVERMAN, B. W. (2005). Functional Data Analysis. Springer Series in Statistics. New York: Springer, 2nd ed.
23. RICE, J. A. (2004). Functional and longitudinal data analysis: Perspectives on smoothing. Statist. Sinica 14, 631-47.
24. RICE, J. A. & SILVERMAN, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B 53, 233-43.
25. STANISWALIS, J. G. & LEE, J. J. (1998). Nonparametric regression analysis of longitudinal data. J. Am. Statist. Assoc. 93, 1403-18.
26. STONE, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705.
27. YAO, F., MÜLLER, H.-G. & WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Am. Statist. Assoc. 100, 577-90.
28. ZHOU, S. & WOLFE, D. A. (2000). On derivative estimation in spline regression. Statist. Sinica 10, 93-108.