Warped functional regression

Biometrika

Volumn 102, Issue 1, 2015, Pages 1-14

  Gervini, Daniel ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Functional data analysis; Random effects model; Registration; Spline smoothing; Time warping

Indexed keywords

EID: 84941568863     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asu054     Document Type: Article

References (26)

1. BRUMBACK, L. C. & LINDSTROM, M. J. (2004). Self modeling with flexible, random time transformations. Biometrics 60, 461-70.
2. CAI, T. & HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 34, 2159-79.
3. CRAMBES, C., KNEIP, A. & SARDA, P. (2009). Smoothing splines estimators for functional linear regression. Ann. Statist. 37, 35-72.
4. FRITSCH, F. N. & CARLSON, R. E. (1980).Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17, 238-46.
5. GERVINI, D. & GASSER, T. (2004). Self-modeling warping functions. J. R. Statist. Soc. B 66, 959-71.
6. GERVINI, D. & GASSER, T. (2005). Nonparametric maximum likelihood estimation of the structural mean of a sample of curves. Biometrika 92, 801-20.
7. GEYER, C. J. (1994). On the asymptotics of constrained M-estimators. Ann. Statist. 22, 1993-2010.
8. HALL, P. & HOROWITZ, J. L. (2007).Methodology and convergence rates for functional linear regression. Ann. Statist. 35, 70-91.
9. JAMES, G. M. (2007). Curve alignment by moments. Ann. Appl. Statist. 1, 480-501.
10. JAMES, G. M., HASTIE, T. J. & SUGAR, C. A. (2000). Principal component models for sparse functional data. Biometrika 87, 587-602.
11. JAMES, G., WANG, J. & ZHU, J. (2009). Functional linear regression that's interpretable. Ann. Statist. 37, 2083-108.
12. JUPP, D. L. B. (1978). Approximation to data by splines with free knots. SIAM J. Numer. Anal. 15, 328-43.
13. KNEIP, A., LI, X., MACGIBBON, B. & RAMSAY, J. O. (2000). Curve registration by local regression. Can. J. Statist. 28, 19-30.
14. KNEIP, A. & RAMSAY, J. O. (2008). Combining registration and fitting for functional models. J. Am. Statist. Assoc. 103, 1155-65.
15. LIU, X. & MÜLLER, H.-G. (2004). Functional convex averaging and synchronization for time-warped random curves. J. Am. Statist. Assoc. 99, 687-99.
16. MAGNUS, J. R. & NEUDECKER, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd ed. New York: Wiley.
17. MÜLLER, H.-G., CHIOU, J.-M. & LENG, X. (2008). Inferring gene expression dynamics via functional regression analysis. BMC Bioinformatics 9, article no. 60.
18. POLLARD, D. (1990). Empirical Processes: Theory and Applications. Hayward, California: Institute of Mathematical Statistics.
19. RAMSAY, J. O. (1988). Monotone regression splines in action (with Discussion). Statist. Sci. 3, 425-61.
20. RAMSAY, J. O. & LI, X. (1998). Curve registration. J. R. Statist. Soc. B 60, 351-63.
21. RAMSAY, J. O. & SILVERMAN, B. W. (2005). Functional Data Analysis, 2nd ed. New York: Springer.
22. ROCKAFELLAR, R. & WETS, R. (1998). Variational Analysis. New York: Springer.
23. TANG, R. & MÜLLER, H.-G. (2008). Pairwise curve synchronization for functional data. Biometrika 95, 875-89.
24. TANG, R. & MÜLLER, H.-G. (2009). Time-synchronized clustering of gene expression trajectories. Biostatistics 10, 32-45.
25. WANG, K. & GASSER, T. (1999). Synchronizing sample curves nonparametrically. Ann. Statist. 27, 439-60.
26. YAO, F., MÜLLER, H.-G. & WANG, J.-L. (2005). Functional linear regression analysis for longitudinal data. Ann. Statist. 33, 2873-903.