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Estimating the complexity index of functional data: Some asymptotics

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  • Bongiorno, E.G.
  • Goia, A.
  • Vieu, P.

Abstract

Consider a random curve valued in a general semi-metric space whose small-ball probability factorizes isolating the spatial and the volumetric term. Assume that the latter is specified and interprets its parameters as complexity indexes. An index estimate is constructed by comparing nonparametric versus parametric estimates of the volumetric factor, and various asymptotics (including weak convergence and asymptotic normality) are stated by means of U-statistics tools. As a by-product, new asymptotic results are stated for surrogate density estimation.

Suggested Citation

  • Bongiorno, E.G. & Goia, A. & Vieu, P., 2020. "Estimating the complexity index of functional data: Some asymptotics," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300341
    DOI: 10.1016/j.spl.2020.108731
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    References listed on IDEAS

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    1. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.
    2. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    3. Frédéric Ferraty & Nadia Kudraszow & Philippe Vieu, 2012. "Nonparametric estimation of a surrogate density function in infinite-dimensional spaces," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 447-464.
    4. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    5. Enea G. Bongiorno & Aldo Goia & Philippe Vieu, 2019. "Modeling functional data: a test procedure," Computational Statistics, Springer, vol. 34(2), pages 451-468, June.
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    Cited by:

    1. Aubin, Jean-Baptiste & Bongiorno, Enea G. & Goia, Aldo, 2022. "The correction term in a small-ball probability factorization for random curves," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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