A test of significance in functional quadratic regression

Bernoulli

Volumn 19, Issue 5 A, 2013, Pages 2120-2151

  Horváth, Lajos ^a   Reeder, Ron ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Absorption spectra; Asymptotics; Functional data analysis; Polynomial regression; Prediction; Principal component analysis

Indexed keywords

EID: 84888322484     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/12-BEJ446     Document Type: Article

References (25)

1. Borggaard, C. and Thodberg, H. (1992). Optimal minimal neural interpretation of spectra. Analytical Chemistry 64 545-551.
2. Bosq, D. (2000). Linear Processes in Function Spaces: Theory and Applications. Lecture Notes in Statistics 149. New York: Springer. MR1783138
3. Cai, T.T. and Hall, P. (2006). Prediction in functional linear regression. Ann. Statist. 34 2159-2179. MR2291496
4. Cardot, H., Ferraty, F., Mas, A. and Sarda, P. (2003). Testing hypotheses in the functional linear model. Scand. J. Statist. 30 241-255. MR1965105
5. Cardot, H., Prchal, L. and Sarda, P. (2007). No effect and lack-of-fit permutation tests for functional regression. Comput. Statist. 22 371-390. MR2336342
6. Cardot, H. and Sarda, P. (2011). Functional linear regression. In The Oxford Handbook of Functional Data Analysis (F. Ferraty and Y. Romain, eds.) 21-46. Oxford: Oxford Univ. Press.
7. Dauxois, J., Pousse, A. and Romain, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. J. Multivariate Anal. 12 136-154. MR0650934
8. Fan, J. and Lin, S.K. (1998). Test of significance when data are curves. J. Amer. Statist. Assoc. 93 1007-1021. MR1649196
9. Ferraty, F. and Romain, Y., eds. (2011). The Oxford Handbook of Functional Data Analysis. Oxford: Oxford Univ. Press. MR2917982
10. Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics. New York: Springer. MR2229687
11. Ferraty, F., Vieu, P. and Viguier-Pla, S. (2007). Factor-based comparison of groups of curves. Comput. Statist. Data Anal. 51 4903-4910. MR2364548
12. Fitzhugh, H.A. (1976). Analysis of growth curves and strategies for altering their shapes. Journal of Animal Science 33 1036-1051.
13. Frank, I.E. and Friedman, J.H. (1993). A statistical view of some chemometrics regression tools. Technometrics 35 109-135.
14. Hall, P. and Horowitz, J.L. (2007). Methodology and convergence rates for functional linear regression. Ann. Statist. 35 70-91. MR2332269
15. Horváth, L. and Kokoszka, P. (2012). Inference for functional data with applications. Preprint.
16. Kirkpatrick, M. and Heckman, N. (1989). A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27 429-450. MR1009899
17. Laukaitis, A. and Račkauskas, A. (2005). Functional data analysis for clients segmentation task. European Journal of Operation Research 163 210-216.
18. Li, B. and Yu, Q. (2008). Classification of functional data: A segmentation approach. Comput. Statist. Data Anal. 52 4790-4800. MR2521623
19. Müller, H.G. and Zhang, Y. (2005). Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories. Biometrics 61 1064-1075. MR2216200
20. Mas, A. and Pumo, B. (2011). Linear processes for functional data. In The Oxford Handbook of Functional Data Analysis (F. Ferraty and Y. Romain, eds.) 47-71. Oxford: Oxford Univ. Press.
21. Ramsay, J.O. and Silverman, B.W. (2005). Functional Data Analysis, 2nd ed. Springer Series in Statistics. New York: Springer. MR2168993
22. Shen, Q. and Faraway, J. (2004). An F test for linear models with functional responses. Statist. Sinica 14 1239-1257. MR2126351
23. Wold, S. (1993). Discussion: PLS in chemical practice. Technometrics 35 136-139.
24. Yao, F. and Müller, H.G. (2010). Functional quadratic regression. Biometrika 97 49-64. MR2594416
25. Zhang, J.T. and Chen, J. (2007). Statistical inferences for functional data. Ann. Statist. 35 1052-1079. MR2341698