Methodology and theory for partial least squares applied to functional data

Annals of Statistics

Volumn 40, Issue 1, 2012, Pages 322-352

  Delaigle, Aurore ^a   Hall, Peter ^a,b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Central limit theorem; Computational algorithm; Consistency; Convergence rates; Functional linear models; Generalized Fourier basis; Principal components; Projection; Stochastic expansion

Indexed keywords

EID: 84870678371     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS958     Document Type: Article

References (35)

1. AGUILERA, M., ESCABIASA, M., PREDA, C. and SAPORTA, G. (2010). Using basis expansions for estimating functional PLS regression: Applications with chemometric data. Chemom. Intell. Lab. 104 289-305.
2. APANASOVICH, T. V. and GOLDSTEIN, E. (2008). On prediction error in functional linear regression. Statist. Probab. Lett. 78 1807-1810. MR25285522
3. BAILLO, A. (2009). A note on functional linear regression. J. Stat. Comput. Simul. 79 657-669. MR25230188
4. BERG, C. and SZWARC, R. (2011). The smallest eigenvalue of Hankel matrices. Constr. Approx. 34 107-133. MR27960933
5. BRO, R. and ELDÉN, L. (2009). PLS works. J. Chemom. 23 69-71.
6. CAI, T. T. and HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 34 2159- 2179. MR22914966
7. CARDOT, H. and SARDA, P. (2008). Varying-coefficient functional linear regression models. Comm. Statist. Theory Methods 37 3186-3203. MR24677600
8. DELAIGLE, A. and HALL, P. (2012). Achieving near-perfect classification for functional data. J. Roy. Statist. Soc. Ser. B 74 267-286.
9. DURAND, J.-F. and SABATIER, R. (1997). Additive splines for partial least squares regression. J. Amer. Statist. Assoc. 92 1546-1554. MR16152644
10. ESCABIAS, M., AGUILERA, A. M. and VALDERRAMA, M. J. (2007). Functional PLS logit regression model. Comput. Statist. Data Anal. 51 4891-4902. MR23645477
11. FERRATY, F. and VIEU, P. (2006). Nonparametric Functional Data Analysis. Springer, New York.
12. FRANK, I. E. and FRIEDMAN, J. H. (1993). A statistical view of some chemometrics regression tools (with discussion). Technometrics 35 109-148.
13. GARTHWAITE, P. H. (1994). An interpretation of partial least squares. J. Amer. Statist. Assoc. 89 122-127. MR12662900
14. GOUTIS, C. and FEARN, T. (1996). Partial least squares regression on smooth factors. J. Amer. Statist. Assoc. 91 627-632. MR13957300
15. HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. Springer, New York. MR27222944
16. HELLAND, I. S. (1990). Partial least squares regression and statistical models. Scand. J. Stat. 17 97-114. MR10859244
17. HÖSKULDSSON, A. (1988). PLS regression methods. J. Chemom. 2 211-228.
18. HOU, Q.-H., LASCOUX, A. and MU, Y.-P. (2005). Evaluation of some Hankel determinants. Adv. in Appl. Math. 34 845-852. MR21290000
19. KRÄMER, N., BOULESTEIX, A. L. and TUTZ, G. (2008). Penalized partial least squares with applications to B-spline transformations and functional data. Chemom. Intell. Lab. 94 60-69.
20. KRÄMER, N. and SUGIYAMA, M. (2011). The degrees of freedom of partial least squares regression. J. Amer. Statist. Assoc. 106 697-705.
21. LANGE, K. (1999). Numerical Analysis for Statisticians. Springer, New York. MR16819633
22. LASCOUX, A. (1990). Inversion des matrices de Hankel. Linear Algebra Appl. 129 77-102. MR10530544
23. LORBER, A., WANGEN, L. E. and KOWALSKI, B. R. (1987). A theoretical foundation for the PLS algorithm. J. Chemom. 1 19-31.
24. MARTENS, H. and NAES, T. (1989). Multivariate Calibration. Wiley, New York. MR10295233
25. MÜLLER, H.-G. and YAO, F. (2010). Additive modelling of functional gradients. Biometrika 97 791-805. MR27461522
26. NGUYEN, D. V. and ROCKE, D. M. (2004). On partial least squares dimension reduction for microarray-based classification: A simulation study. Comput. Statist. Data Anal. 46 407-425. MR20670300
27. PHATAK, A. and DE HOOG, F. (2003). Exploiting the connection between PLS, Lanczos, and conjugate gradients: Alternative proofs of some properties of PLS. J. Chemom. 16 361-367.
28. PHATAK, A., REILLY, P. M. and PENLIDIS, A. (2002). The asymptotic variance of the univariate PLS estimator. Linear Algebra Appl. 354 245-253. MR19276600
29. PREDA, C. and SAPORTA, G. (2005a). PLS regression on a stochastic process. Comput. Statist. Data Anal. 48 149-158. MR21344888
30. PREDA, C. and SAPORTA, G. (2005b). Clusterwise PLS regression on a stochastic process. Comput. Statist. Data Anal. 49 99-108. MR21291677
31. PREDA, C., SAPORTA, G. and LÉVÉDER, C. (2007). PLS classification of functional data. Comput. Statist. 22 223-235. MR23184577
32. REISS, P. T. and OGDEN, R. T. (2007). Functional principal component regression and functional partial least squares. J. Amer. Statist. Assoc. 102 984-996. MR24116600
33. WOLD, H. (1975). Soft modelling by latent variables: The non-linear iterative partial least squares (NIPALS) approach. In Perspectives in Probability and Statistics, Papers in Honour of M. S. Bartlett (J. Gani, ed.). Academic Press, London.
34. WU, Y., FAN, J. and MÜLLER, H.-G. (2010). Varying-coefficient functional linear regression. Bernoulli 16 730-758. MR27306466
35. YAO, F. and MÜLLER, H.-G. (2010). Functional quadratic regression. Biometrika 97 49-64. MR25944166