# On the Effect of Curve Alignment and Functional PCA

• Juhyun Park
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

When dealing with multiple curves as functional data, it is a common practice to apply functional PCA to summarise and characterise random variation infinite dimension. Often functional data however exhibits additional time variability that distorts the assumed common structure. This is recognized as the problem of curve registration. While the registration step is routinely employed, this is considered as a preprocessing step prior to any serious analysis. Consequently, the effect of alignment is mostly ignored in subsequent analyses and is not well understood. We revisit the issue by particularly focusing on the effect of time variability on the FPCA and illustrate the phenomena from a borrowed perturbation viewpoint. The analysis further suggests an iterative estimating procedure to optimise FPCA.

## Keywords

Functional Data American Statistical Association Time Variability Functional Data Analysis Longitudinal Data Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
Dauxois, J. Pousse, A. and Romain, Y.: Asymptotic theory for the principal compo-nent analysis of a vector random function: some applications to statistical inference. Journal of Multivariate Analysis, 12, 136-154 (1982).
2. [2]
Liu, X. and Müller, H. G.: Functional convex averaging and synchronization for time-warped random curves. Journal of the American Statistical Association, 99, 687-699 (2004).
3. [3]
Gasser, T. and Kneip, A.: Searching for structure in curve samples. Journal of the American Statistical Association, 90, 1179-1188 (1995).
4. [4]
Hall, P, Müller, H. G. and Wang, J. L.: Properties of principal componenet methods for functional and longitudinal data analysis. Annals of Statistics, 34, 1493-1517 (2006).
5. [5]
Kneip, A.: Nonparametric estimation of common regressors for similar curve data. Annals of Statistics, 22, 1386-1427 (1994).
6. [6]
Kneip, A. and Ramsay, J. O.: Combining registration and tting for functional mod-els. technical report. (2007).Google Scholar
7. [7]
Park, J. Gasser, T. and Rousson, V.: Structural components in functional data. technical report. (2007).Google Scholar
8. [8]
Ramsay, J. O. and Silverman, B. W.: Applied functional data analysis, New York: Springer. (2002).
9. [9]
Ramsay, J. O. and Silverman, B. W.: Functional data analysis, New York: Springer. (2005).Google Scholar
10. [10]
Rice, J. W. and Silverman, B. W.: Estimating the mean and the covariance structure nonparametrically when the data are curves. Journal of Royal Statistical Society, B, 53,233-243 (1991).