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Kernel-based functional principal components

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  • Boente, Graciela
  • Fraiman, Ricardo
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    Abstract

    In this paper, we propose kernel-based smooth estimates of the functional principal components when data are continuous trajectories of stochastic processes. Strong consistency and the asymptotic distribution are derived under mild conditions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 48 (2000)
    Issue (Month): 4 (July)
    Pages: 335-345

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    Handle: RePEc:eee:stapro:v:48:y:2000:i:4:p:335-345

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    Related research

    Keywords: Functional principal components Kernel methods Hilbert-Schmidt operators Eigenfunctions;

    References

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    1. Fraiman, Ricardo & Iribarren, Gonzalo Pérez, 1991. "Nonparametric regression estimation in models with weak error's structure," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 180-196, May.
    2. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer, vol. 51(2), pages 285-311, June.
    3. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer, vol. 47(4), pages 379-396, December.
    4. 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, Elsevier, vol. 12(1), pages 136-154, March.
    5. Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
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    Citations

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    Cited by:
    1. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," Advances in Data Analysis and Classification, Springer, vol. 6(3), pages 219-247, October.
    2. 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.
    3. Benhenni, K. & Hedli-Griche, S. & Rachdi, M., 2010. "Estimation of the regression operator from functional fixed-design with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 476-490, February.
    4. Idir Ouassou & Mustapha Rachdi, 2012. "Regression operator estimation by delta-sequences method for functional data and its applications," AStA Advances in Statistical Analysis, Springer, vol. 96(4), pages 451-465, October.
    5. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    6. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    7. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2010. "Inference under functional proportional and common principal component models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 464-475, February.
    8. Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer, vol. 98(3), pages 257-286, July.
    9. Huang, Lele & Wang, Huiwen & Zheng, Andi, 2014. "The M-estimator for functional linear regression model," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 165-173.
    10. Park, Juhyun & Gasser, Theo & Rousson, Valentin, 2009. "Structural components in functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3452-3465, July.
    11. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    12. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.

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