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Repeated measures analysis for functional data

  • Martínez-Camblor, Pablo
  • Corral, Norberto
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    Most of the traditional statistical methods are being adapted to the Functional Data Analysis (FDA) context. The repeated measures analysis which deals with the k-sample problem when the data are from the same subjects is investigated. Both the parametric and the nonparametric approaches are considered. Asymptotic, permutation and bootstrap approximations for the statistic distribution are developed. In order to explore the statistical power of the proposed methods in different scenarios, a Monte Carlo simulation study is carried out. The results suggest that the studied methodology can detect small differences between curves even with small sample sizes.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002106
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 12 (December)
    Pages: 3244-3256

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3244-3256
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Epifanio, Irene & Ventura-Campos, Noelia, 2011. "Functional data analysis in shape analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2758-2773, September.
    2. Frédéric Ferraty & Ingrid Van Keilegom & Philippe Vieu, 2010. "On the Validity of the Bootstrap in Non-Parametric Functional Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 286-306.
    3. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    4. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    5. Pedro Delicado, 2007. "Functional k-sample problem when data are density functions," Computational Statistics, Springer, vol. 22(3), pages 391-410, September.
    6. 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.
    7. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    8. Park, Juhyun & Gasser, Theo & Rousson, Valentin, 2009. "Structural components in functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3452-3465, July.
    9. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.
    10. André Mas, 2007. "Testing for the Mean of Random Curves: A Penalization Approach," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 147-163, 07.
    11. Martínez-Camblor, Pablo & de Uña-Álvarez, Jacobo, 2009. "Non-parametric k-sample tests: Density functions vs distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3344-3357, July.
    12. Rosen, Ori & Thompson, Wesley K., 2009. "A Bayesian regression model for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3773-3786, September.
    13. 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.
    14. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    15. 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.
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