IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i2d10.1007_s00362-015-0710-2.html
   My bibliography  Save this article

On linear regression models in infinite dimensional spaces with scalar response

Author

Listed:
  • Andrea Ghiglietti

    (Università degli Studi di Milano)

  • Francesca Ieva

    (Università degli Studi di Milano)

  • Anna Maria Paganoni

    (Politecnico di Milano)

  • Giacomo Aletti

    (Università degli Studi di Milano)

Abstract

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem, which has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on finite-dimensional subspaces. We discuss the standard approach based explicitly on functional principal components analysis, nevertheless the choice of the number of basis components remains something subjective and not always properly discussed and justified. In this work we discuss inferential properties of least square estimation in this context, with different choices of projection subspaces, as well as we study asymptotic behaviour increasing the dimension of subspaces.

Suggested Citation

  • Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni & Giacomo Aletti, 2017. "On linear regression models in infinite dimensional spaces with scalar response," Statistical Papers, Springer, vol. 58(2), pages 527-548, June.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0710-2
    DOI: 10.1007/s00362-015-0710-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0710-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0710-2?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. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    Full references (including those not matched with items on IDEAS)

    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. Mirosław Krzyśko & Łukasz Smaga, 2017. "An Application Of Functional Multivariate Regression Model To Multiclass Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 433-442, September.
    2. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    3. Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.
    4. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Tomasz Górecki & Mirosław Krzyśko & Łukasz Waszak & Waldemar Wołyński, 2018. "Selected statistical methods of data analysis for multivariate functional data," Statistical Papers, Springer, vol. 59(1), pages 153-182, March.
    6. Fabrizio Maturo & Rosanna Verde, 2023. "Supervised classification of curves via a combined use of functional data analysis and tree-based methods," Computational Statistics, Springer, vol. 38(1), pages 419-459, March.
    7. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
    8. Górecki Tomasz & Krzyśko Mirosław & Wołyński Waldemar, 2015. "Classification Problems Based on Regression Models for Multi-Dimensional Functional Data," Statistics in Transition New Series, Statistics Poland, vol. 16(1), pages 97-110, March.
    9. 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.
    10. Gertheiss, Jan & Goldsmith, Jeff & Staicu, Ana-Maria, 2017. "A note on modeling sparse exponential-family functional response curves," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 46-52.
    11. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Brian Kwan & Catherine A. Sugar & Qi Qian & Frederick Shic & Adam Naples & Scott P. Johnson & Sara J. Webb & Shafali Jeste & Susan Faja & April R. Levin & Geraldine Dawson & James C. McPartland & Daml, 2024. "Constrained Multivariate Functional Principal Components Analysis for Novel Outcomes in Eye-Tracking Experiments," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 578-603, December.
    13. Qiu, Zhiping & Fan, Jiangyuan & Zhang, Jin-Ting & Chen, Jianwei, 2024. "Tests for equality of several covariance matrix functions for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    14. Qi Qian & Danh V. Nguyen & Esra Kürüm & Connie M. Rhee & Sudipto Banerjee & Yihao Li & Damla Şentürk, 2024. "Multivariate Varying Coefficient Spatiotemporal Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 761-786, December.
    15. Tin Lok James Ng & Thomas Brendan Murphy, 2021. "Model-based Clustering of Count Processes," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 188-211, July.
    16. Krzyśko Mirosław & Smaga Łukasz, 2017. "An Application of Functional Multivariate Regression Model to Multiclass Classification," Statistics in Transition New Series, Statistics Poland, vol. 18(3), pages 433-442, September.
    17. Shan Zhong & David B. Hitchcock, 2024. "Functional clustering of fictional narratives using Vonnegut curves," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(4), pages 1045-1066, December.
    18. Tomasz Górecki & Mirosław Krzyśko & Waldemar Wołyński, 2015. "Classification Problems Based On Regression Models For Multi-Dimensional Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 16(1), pages 97-110, March.
    19. 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).
    20. Mirosław Krzyśko & Peter Nijkamp & Waldemar Ratajczak & Waldemar Wołyński, 2022. "Multidimensional economic indicators and multivariate functional principal component analysis (MFPCA) in a comparative study of countries’ competitiveness," Journal of Geographical Systems, Springer, vol. 24(1), pages 49-65, January.

    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:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0710-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.