Functional singular component analysis

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 73, Issue 3, 2011, Pages 303-324

  Yang, Wenjing ^a   Müller, Hans Georg ^a   Stadtmüller, Ulrich ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

Bivariate stochastic process; Functional correlation; Functional data analysis; Longitudinal data; Principal component; Singular component; Singular value decomposition

Indexed keywords

EID: 79955036673     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2010.00769.x     Document Type: Article

References (27)

1. Baker, C. R. (1974) Joint measures and cross-covariance operators. Trans. Am. Math. Soc., 186, 273-289.
2. Bapna, R., Jank, W. and Shmueli, G. (2008) Price formation and its dynamics in online auctions. Decisn Supp. Syst., 44, 641-656.
3. Cupidon, J., Eubank, R., Gilliam, D. and Ruymgaart, F. (2008) Some properties of canonical correlations and variates in infinite dimensions. J. Multiv. Anal., 99, 1083-1104.
4. Dubin, J. A. and Müller, H.-G. (2005) Dynamical correlation for multivariate longitudinal data. J. Am. Statist. Ass., 100, 872-881.
5. Eubank, R. L. and Hsing, T. (2008) Canonical correlation for stochastic processes. Stoch. Processes Applic., 118, 1634-1661.
6. Ghebreab, S., Smeulders, A. W. M. and Adriaans, P. (2007) Predictive modeling of fmri brain states using functional canonical correlation analysis. In Lect. Notes Artif. Intell., 4594, 1-8.
7. Gualtierotti, A. F. (1979) On cross-covariance operators. SIAM. J. Appl. Math., 37, 325-329.
8. Hannan, E. J. (1961) The general theory of canonical correlation and its relation to functional analysis. J. Aust. Math. Soc. A, 2, 229-242.
9. He, G., Müller, H.-G. and Wang, J.-L. (2003) Functional canonical analysis for square integrable stochastic processes. J. Multiv. Anal., 85, 54-77.
10. He, G., Müller, H.-G. and Wang, J.-L. (2004) Methods of canonical analysis for functional data. J. Statist. Planng Inf., 122, 141-159.
11. Heckman, N. E. and Zamar, R. H. (2000) Comparing the shapes of regression functions. Biometrika, 87, 135-144.
12. Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321-377.
13. Jank, W. and Shmueli, G. (2006) Functional data analysis in electronic commerce research. Statist. Sci., 21, 155-166.
14. Kato, T. (1995) Perturbation Theory for Linear Operators. Berlin: Springer.
15. Leurgans, S. E., Moyeed, R. A. and Silverman, B. W. (1993) Canonical correlation analysis when the data are curves. J. R. Statist. Soc. B, 55, 725-740.
16. Liu, B. and Müller, H.-G. (2008) Functional data analysis for sparse auction data. In Statistical Methods in eCommerce Research (eds W. Jank and G. Shmueli ), pp. 269-290. New York: Wiley.
17. Preda, C. and Saporta, G. (2005) PLS regression on a stochastic process. Computnl Statist. Data Anal., 48, 149-158.
18. Ramsay, J. O. and Silverman, B. W. (2005) Functional Data Analysis, 2nd edn. New York: Springer.
19. Rice, J. A. and Silverman, B. W. (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B, 53, 233-243.
20. Service, S. K., Rice, J. A. and Chavez, F. P. (1998) Relationship between physical and biological variables during the upwelling period in Monterey Bay. Deep Sea Res. II, 45, 1669-1685.
21. Shmueli, G. and Jank, W. (2005) Visualizing online auctions. J. Computnl Graph. Statist., 14, 299-319.
22. Shock, N. W., Greulich, R. C., Andres, R., Lakatta, E. G., Arenberg, D. and Tobin, J. D. (1984) Normal human aging: the Baltimore Longitudinal Study of Aging. NIH Publ. 84-2450. Government Printing Office, Washington DC.
23. Silverman, B. W. (1996) Smoothed functional principal components analysis by choice of norm. Ann. Statist., 24, 1-24.
24. Wegelin, J. A. (2000) A survey of partial least squares (PLS) methods, with emphasis on the two-block case. Technical Report. Department of Statistics, University of Washington, Seattle.
25. Witten, D. M., Tibshirani, R. and Hastie, T. (2009) A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics, 10, 515-534.
26. Yao, F., Müller, H.-G. and Wang, J.-L. (2005a) Functional linear regression analysis for longitudinal data. Ann. Statist., 33, 2873-2903.
27. Yao, F., Müller, H.-G. and Wang, J.-L. (2005b) Functional data analysis for sparse longitudinal data. J. Am. Statist. Ass., 100, 577-590.