Location of Repository

Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied

Year: 2009

OAI identifier:
oai:eprints.lancs.ac.uk:20799

Provided by:
Lancaster E-Prints

Downloaded from
http://eprints.lancs.ac.uk/20799/1/sca_Jul07.pdf

- (1987). Analysis of linear growth using a mathematical model ii. from 3 to 21 years of age.
- (2002). Applied Functional Data Analysis: Methods and Case Studies.
- (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference.
- (2004). Criteria for evaluating dimension-reducing components for multivariate data.
- (2005). Functional data analysis for sparse longitudinal data.
- (1997). Functional Data Analysis.
- (2000). Kernel-based functional principal components.
- (1968). Linear Statistical Inference and its Applications.
- (2002). Local polynomial mixed-eﬀects models for longitudinal data.
- (1991). Modelization, nonparametric estimation and prediction for continuous time processes.
- (1998). Nonparametric estimation of covariance structure in longitudinal data.
- (2000). Nonparametric estimation of smoothed principal components analysis of sampled noisy functions.
- (1984). Nonparametric regression analysis of growth curves.
- (1998). Nonparametric regression analysis of longitudinal data.
- (1987). On the modeling of human growth.
- (1980). Shape-invariant modeling of human growth.
- (2003). Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate.
- (2004). Simple component analysis.
- (1996). Smoothed functional principal component analysis by choice of norm.
- (1992). Statistical tools to analyze data representing a sample of curves.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.