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Structural components in functional data

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  • Park, Juhyun
  • Gasser, Theo
  • Rousson, Valentin

Abstract

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.

Suggested Citation

  • Park, Juhyun & Gasser, Theo & Rousson, Valentin, 2009. "Structural components in functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3452-3465, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3452-3465
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    References listed on IDEAS

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    1. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    2. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    3. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    4. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.

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