References
Besse, P., & Ramsay, J. O. (1986). Principal components analysis of sampled functions. Psychometrika, 51, 285–311.
Castro, P. E., Lawton, W. H., & Sylvestre, E. A. (1986). Principal modes of variation for processes with continuous sample curves. Technometrics, 28, 329–337.
Chiou, J.-M., & Müller, H.-G. (2009). Modeling hazard rates as functional data for the analysis of cohort lifetables and mortality forecasting. Journal of the American Statistical Association 104, 572–585.
Dauxois, J., Pousse, A., & Romain, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. Journal of Multivariate Analysis, 12, 136–154.
Grenander, U. (1950). Stochastic processes and statistical inference. Arkiv för Matematik, 1, 195–277.
Müller, H.-G., Wang, J.-L., & Capra, W. B. (1997). From lifetables to hazard rates: The transformation approach. Biometrika, 84, 881–892.
Ramsay, J. O., & Silverman, B. W. (1997). Functional data analysis. New York: Springer-Verlag Inc..
Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 1–17.
Rice, J. A., & Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 53, 233–243.
Vaupel, J. W., Carey, J. R., Christensen, K., Johnson, T. E., Yashin, A. I., Holm, N. V., et al. (1998). Biodemographic trajectories of longevity. Science, 280, 855–860.
Wang, J.-L. (2005). Smoothing hazard rate. In Encyclopedia of biostatistics, vol. 7 (2nd ed.) (pp. 4986–4997). New York: Wiley.
Wang, J.-L., Müller, H.-G., & Capra, W. B. (1998). Analysis of oldest-old mortality: Lifetables revisited. The Annals of Statistics, 26, 126–163.
Yao, F., Müller, H.-G., & Wang, J.-L. (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100, 577–590.
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This research was supported in part by grants from the National Science Council (NSC95-2118M001-013MY3) and the National Science Foundation (DMS-086199, DMS-046430).
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Chiou, JM., Müller, HG. & Wang, JL. Discussion: Forecasting functional time series. J. Korean Stat. Soc. 38, 213–215 (2009). https://doi.org/10.1016/j.jkss.2009.05.005
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DOI: https://doi.org/10.1016/j.jkss.2009.05.005