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Modeling functional data: a test procedure

Author

Listed:
  • Enea G. Bongiorno

    (Università del Piemonte Orientale)

  • Aldo Goia

    (Università del Piemonte Orientale)

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

The paper deals with a test procedure able to state the compatibility of observed data with a reference model, by using an estimate of the volumetric part in the small-ball probability factorization which plays the role of a real complexity index. As a preliminary by-product we state some asymptotics for a new estimator of the complexity index. A suitable test statistic is derived and, referring to the U-statistics theory, its asymptotic null distribution is obtained. A study of level and power of the test for finite sample sizes and a comparison with a competitor are carried out by Monte Carlo simulations. The test procedure is performed over a financial time series.

Suggested Citation

  • Enea G. Bongiorno & Aldo Goia & Philippe Vieu, 2019. "Modeling functional data: a test procedure," Computational Statistics, Springer, vol. 34(2), pages 451-468, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0816-9
    DOI: 10.1007/s00180-018-0816-9
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    References listed on IDEAS

    as
    1. Bongiorno, Enea G. & Goia, Aldo, 2016. "Classification methods for Hilbert data based on surrogate density," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 204-222.
    2. Cuesta-Albertos, J.A. & del Barrio, E. & Fraiman, R. & Matran, C., 2007. "The random projection method in goodness of fit for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4814-4831, June.
    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. Yen, Gili & Yen, Eva C, 1999. "On the Validity of the Wiener Process Assumption in Option Pricing Models: Contradictory Evidence from Taiwan," Review of Quantitative Finance and Accounting, Springer, vol. 12(4), pages 327-340, June.
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    Cited by:

    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. Bongiorno, E.G. & Goia, A. & Vieu, P., 2020. "Estimating the complexity index of functional data: Some asymptotics," Statistics & Probability Letters, Elsevier, vol. 161(C).
    3. 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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