IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v161y2020ics0167715220300341.html
   My bibliography  Save this article

Estimating the complexity index of functional data: Some asymptotics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220300341
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108731?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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).
    2. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Febrero-Bande, Manuel & Galeano, Pedro & González-Manteiga, Wenceslao, 2019. "Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 91-103.
    4. Mustapha Rachdi & Ali Laksaci & Zoulikha Kaid & Abbassia Benchiha & Fahimah A. Al‐Awadhi, 2021. "k‐Nearest neighbors local linear regression for functional and missing data at random," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 42-65, February.
    5. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    6. Ali Laksaci & Elias Ould Saïd & Mustapha Rachdi, 2021. "Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 895-911, August.
    7. Amel, Azzi & Ali, Laksaci & Elias, Ould Saïd, 2022. "On the robustification of the kernel estimator of the functional modal regression," Statistics & Probability Letters, Elsevier, vol. 181(C).
    8. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    9. Wenjuan Hu & Nan Lin & Baoxue Zhang, 2020. "Nonparametric testing of lack of dependence in functional linear models," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-24, June.
    10. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    11. 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.
    12. Zhang, Xiaoke & Wang, Jane-Ling, 2018. "Optimal weighting schemes for longitudinal and functional data," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 165-170.
    13. Febrero-Bande, Manuel & González-Manteiga, Wenceslao & Prallon, Brenda & Saporito, Yuri F., 2023. "Functional classification of bitcoin addresses," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    14. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    15. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    16. Fermanian, Adeline, 2021. "Embedding and learning with signatures," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    17. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    18. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    19. Sigve Hovda, 2014. "Using pseudometrics in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 669-696, December.
    20. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300341. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.