Functional canonical analysis for square integrable stochastic processes

Journal of Multivariate Analysis

Volumn 85, Issue 1, 2003, Pages 54-77

  He, Guozhong ^a   Müller, Hans Georg ^b   Wang, Jane Ling ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Canonical correlation; Canonical decomposition; Covariance operator; Functional data analysis; Hilbert Schmidt operator; Inverse problem

Indexed keywords

EID: 0038734117     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00056-8     Document Type: Article

References (14)

1. R.B. Ash, M.F. Gardner, Topics in Stochastic Processes, Academic Press, New York, 1975.
2. D.R. Brillinger, Time Series. Data Analysis and Theory, Holt, Rinehart and Winston, New York, 1975.
3. J.B. Conway, A Course in Functional Analysis, Springer, New York, 1985.
4. J. Dauxois, G.M. Nkiet, Canonical analysis of two Euclidean subspaces and its applications, Linear Algebra Appl. 264 (1997) 355-388.
5. N. Dunford, J.T. Schwartz, Linear Operators, Parts I and II, Wiley, New York, 1988.
6. E.J. Hannan, The general theory of canonical correlation and its relation to functional analysis, J. Austral. Math. Soc. 2 (1961) 229-242.
7. G. He, H.-G. Müller, J.-L. Wang, Extending correlation and regression from multivariate to functional data, in: M. Puri (Ed.), Asymptotics in Statistics and Probability VSP, Zeist (Netherlands), 2000, pp. 197-210.
8. G. He, H.-G. Müller, J.-L. Wang, Functional linear modelling and canonical regression analysis, 2002, UC Davis, Manuscript.
9. H. Hotelling, Relations between two sets of variates, Biometrika 28 (1936) 321-377.
10. S.E. Leurgans, R.A. Moyeed, B.W. Silverman, Canonical correlation analysis when the data are curves, J. R. Statist. Soc. B 55 (1993) 725-740.
11. R.A. Olshen, E.N. Biden, M.P. Wyatt, D.H. Sutherland, Gait analysis and the bootstrap, Ann. Statist. 17 (1989) 1419-1440.
12. J.O. Ramsay, B.W. Silverman, Functional Data Analysis, Springer, New York, 1997.
13. J.A. Rice, B.W. Silverman, Estimating the mean and covariance structure nonparametrically when the data are curves, J. Roy. Statist. Soc. B 53 (1991) 233-243.
14. S.K. Service, J.A. Rice, F.P. Chavez, Relationship between physical and biological variables during the upwelling period in Monterey Bay, CA, Deep-Sea Research II Vol. 45, (1998) 1669-1685.