Functional variance processes

Journal of the American Statistical Association

Volumn 101, Issue 475, 2006, Pages 1007-1018

  Müller, Hans Georg ^a   Stadtmüller, Ulrich ^b   Fang, Y A O ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ULM   (Germany)

^c Department of Ecosystem Science and Sustainability   (United States)

Author keywords

Eigenfunction; Functional data analysis; Principal component; Random trajectory; Variance function

Indexed keywords

EID: 33748870923     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000000186     Document Type: Review

References (29)

1. Carey, J., Liedo, P., Müller, H. G., Wang, J. L., and Chiou, J. M. (1998). "Relationship of Age Patterns of Fecundity to Mortality, Longevity and Lifetime Reproduction in a Large Cohort of Mediterranean Fruit Fly Females," Journal of Gerontology-Biological Sciences. 53, 245-251.
2. Castro, P. E., Lawton, W. H., and Sylvestre, E. A. (1986), "Principal Modes of Variation for Processes With Continuous Sample Curves," Technometrics, 28, 329-337.
3. Chiou, J. M., and Müller, H. G. (1999), "Nonparametric Quasi-Likelihood," The Annals of Statistics, 27, 36-64.
4. Courant, R. and Hilbert, D. (1989), Methods of Mathematical Physics, New York: Wiley.
5. Dette, H., and Munk, A. (1998). "Testing Heteroscedasticity in Nonparametric Regression," Journal of the Royal Statistical Society, Ser. B, 60, 693-708.
6. Euhank, R., and Thomas, W. (1993), "Detecting Heteroscedasticity in Nonparametric Regression," Journal of the Royal Statistical Society, Ser. B, 55, 145-155.
7. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications. London: Chapman & Hall.
8. Fan. J. Q., and Yao, Q. W. (1998), "Efficient Estimation of Conditional Variance Functions in Stochastic Regression," Biometrika, 85, 645-660.
9. Gasser, T., Sroka, L., and Jennen-Steinmetz., C. ( 1986), "Residual Variance and Residual Patterns in Nonlinear Regression," Biometrika, 73, 625-633.
10. Grenander, U. (1950). "Stochastic Processes and Statistical Inference," Arkiv för Matematik. 195-276.
11. Hall, P., Poskitt, D. S., and Presnell, B. (2001), "A Functional Data-Analytic Approach to Signal Discrimination," Technometrics, 43, 1-9.
12. James, G., Hastie, T. G., and Sugar, C. A. (2001), "Principal Component Models for Sparse Functional Data," Biometrika, 87, 587-602.
13. Jones, M. C., and Rice, J. (1992), "Displaying the Important Features of Large Collections of Similar Curves," The American Statistician. 46, 140-145.
14. Kakizawa, Y., Shumway, R. H., and Tanaguchi, M. (1998), "Discrimination and Clustering for Multivariate Time Series," Journal of the American Statistical Association, 441, 328-340.
15. Müller, H. G., and Stadtmüller, U. (1987), "Estimation of Heteroscedasticity in Regression Analysis," The Annals of Statistics, 15, 610-625.
16. Müller, H. G., and Zhao, P. L. (1995), "On a Semiparametric Variance Function Model and a Test for Heteroscedasticity," The Annals of Statistics, 23, 946-967.
17. Ramsay, J. O., and Silverman, B. W. (2002), Applied Functional Data Analysis, New York: Springer-Verlag.
18. _ (2005). Functional Data Analysis, New York: Springer-Verlag.
19. Rao, C. R. (1958), "Some Statistical Models for Comparison of Growth Curves," Biometrics, 14, 1-17.
20. Rice, J. A., and Silverman, B. W. (1991), "Estimating the Mean and Covariance Structure Nonparametrically When the Data Are Curves," Journal of the Royal Statistical Society, Ser. B. 53, 233-243.
21. Schuster, E., and Yakowitz, S. (1979), "Contributions to the Theory of Nonparametric Regression, With Application to System Identification," The Annals of Statistics, 7, 139-149.
22. Shumway, R. H. (2002), "Time-Frequency Clustering and Discriminant Analysis," in Computing Science and Statistics - Geoscience and Remote Sensing, Proceedings of the Interface, Vol. 34, eds. E. J. Wegman and A. Braverman, Fairfax Station: Interface Foundation of North America, pp. 373-379.
23. Staniswalis, J. G., and Lee, J. J. (1998), "Nonparametric Regression Analysis of Longitudinal Data," Journal of the American Statistical Association, 93, 1403-1418.
24. Wedderburn, R. W. M. (1974), "Quasi-Likelihood Functions, Generalized Linear Models and Gauss-Newton Method," Biometrika, 61, 439-447.
25. Yao, F., and Lee, T. C. M. (2006), "Penalized Spline Models for Functional Principal Component Analysis," Journal of the Royal Statistical Society, Ser. B, 68, 3-25.
26. Yao, F., Müller, H. G., Clifford, A. J., Dueker, S. R., Follett, J., Lin, Y. Buchholz, B., and Vogel, J. S. (2003), "Shrinkage Estimation for Functional Principal Component Scores, With Application to the Population Kinetics of Plasma Folate," Biometrics, 59, 676-685.
27. Yao, F., Müller, H. G., and Wang, J. L. (2005), "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, 100, 577-590.
28. Yao, Q. W., and Tong, H. (2000), "Nonparametric Estimation of Ratios of Noise to Signal in Stochastic Regression," Statistica Sinica, 10, 751-770.
29. Yu, K., and Jones, M. C. (2004), "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association. 99, 139-144.