IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v72y2020i4d10.1007_s10463-019-00718-2.html
   My bibliography  Save this article

Regression function estimation as a partly inverse problem

Author

Listed:
  • F. Comte

    (University Paris Descartes)

  • V. Genon-Catalot

    (University Paris Descartes)

Abstract

This paper is about nonparametric regression function estimation. Our estimator is a one-step projection estimator obtained by least-squares contrast minimization. The specificity of our work is to consider a new model selection procedure including a cutoff for the underlying matrix inversion, and to provide theoretical risk bounds that apply to non-compactly supported bases, a case which was specifically excluded of most previous results. Upper and lower bounds for resulting rates are provided.

Suggested Citation

  • F. Comte & V. Genon-Catalot, 2020. "Regression function estimation as a partly inverse problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1023-1054, August.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00718-2
    DOI: 10.1007/s10463-019-00718-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-019-00718-2
    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/s10463-019-00718-2?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. Fabienne Comte & Charles-A. Cuenod & Marianna Pensky & Yves Rozenholc, 2017. "Laplace deconvolution on the basis of time domain data and its application to dynamic contrast-enhanced imaging," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 69-94, January.
    2. Denis Belomestny & Fabienne Comte & Valentine Genon-Catalot, 2019. "Sobolev-Hermite versus Sobolev nonparametric density estimation on $${\mathbb {R}}$$ R," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 29-62, February.
    3. Sandra Plancade, 2011. "Model selection for hazard rate estimation in presence of censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 313-347, November.
    4. Gwennaëlle Mabon, 2017. "Adaptive Deconvolution on the Non-negative Real Line," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 707-740, September.
    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. Kare Kamila, 2023. "Data-driven model selection for same-realization predictions in autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 567-592, August.
    2. Nicolas Marie, 2023. "Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models," Finance and Stochastics, Springer, vol. 27(1), pages 97-126, January.
    3. Comte, Fabienne & Marie, Nicolas, 2023. "Nonparametric drift estimation from diffusions with correlated Brownian motions," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    4. Comte, Fabienne & Genon-Catalot, Valentine, 2021. "Drift estimation on non compact support for diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 174-207.
    5. Florian Dussap, 2023. "Nonparametric multiple regression by projection on non-compactly supported bases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 731-771, October.

    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. Comte, Fabienne & Genon-Catalot, Valentine, 2021. "Drift estimation on non compact support for diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 174-207.
    2. Denis Belomestny & Fabienne Comte & Valentine Genon-Catalot, 2019. "Sobolev-Hermite versus Sobolev nonparametric density estimation on $${\mathbb {R}}$$ R," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 29-62, February.
    3. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation on non compact support in an heteroscesdastic model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 93-128, January.
    4. Fabienne Comte & Gwennaelle Mabon & Adeline Samson, 2017. "Spline regression for hazard rate estimation when data are censored and measured with error," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(2), pages 115-140, May.
    5. Gwennaëlle Mabon, 2017. "Adaptive Deconvolution on the Non-negative Real Line," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 707-740, September.
    6. Pawan Gupta & Marianna Pensky, 2018. "Solution of Linear Ill-Posed Problems Using Random Dictionaries," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 178-193, May.
    7. Fabienne Comte & Nicolas Marie, 2021. "Nonparametric estimation for I.I.D. paths of fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 669-705, October.

    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:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00718-2. 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.