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Wavelets in functional data analysis: Estimation of multidimensional curves and their derivatives

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  • Pigoli, Davide
  • Sangalli, Laura M.

Abstract

A wavelet-based method is proposed to obtain accurate estimates of curves in more than one dimension and of their derivatives. By means of simulation studies, this novel method is compared to another locally-adaptive estimation technique for multidimensional functional data, based on free-knot regression splines. This comparison shows that the proposed method is particularly attractive when the curves to be estimated present strongly localized features. The multidimensional wavelet estimation method is thus applied to multi-lead electrocardiogram records, where strongly localized features are indeed expected.

Suggested Citation

  • Pigoli, Davide & Sangalli, Laura M., 2012. "Wavelets in functional data analysis: Estimation of multidimensional curves and their derivatives," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1482-1498.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1482-1498 DOI: 10.1016/j.csda.2011.12.016
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    References listed on IDEAS

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    1. Wang, Xiaohui & Ray, Shubhankar & Mallick, Bani K., 2007. "Bayesian Curve Classification Using Wavelets," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 962-973, September.
    2. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    3. Laura M. Sangalli & Piercesare Secchi & Simone Vantini & Alessandro Veneziani, 2009. "Efficient estimation of three-dimensional curves and their derivatives by free-knot regression splines, applied to the analysis of inner carotid artery centrelines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 285-306.
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    Cited by:

    1. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    2. Aletti, Giacomo & May, Caterina & Tommasi, Chiara, 2016. "Best estimation of functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 54-68.
    3. repec:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0269-3 is not listed on IDEAS

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