IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v46y2019i2p517-544.html
   My bibliography  Save this article

Score estimation in the monotone single‐index model

Author

Listed:
  • Fadoua Balabdaoui
  • Piet Groeneboom
  • Kim Hendrickx

Abstract

We consider estimation in the single‐index model where the link function is monotone. For this model, a profile least‐squares estimator has been proposed to estimate the unknown link function and index. Although it is natural to propose this procedure, it is still unknown whether it produces index estimates that converge at the parametric rate. We show that this holds if we solve a score equation corresponding to this least‐squares problem. Using a Lagrangian formulation, we show how one can solve this score equation without any reparametrization. This makes it easy to solve the score equations in high dimensions. We also compare our method with the effective dimension reduction and the penalized least‐squares estimator methods, both available on CRAN as R packages, and compare with link‐free methods, where the covariates are elliptically symmetric.

Suggested Citation

  • Fadoua Balabdaoui & Piet Groeneboom & Kim Hendrickx, 2019. "Score estimation in the monotone single‐index model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 517-544, June.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:2:p:517-544
    DOI: 10.1111/sjos.12361
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12361
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12361?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
    ---><---

    Citations

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


    Cited by:

    1. Yoichi Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under Monotone Heteroskedasticity," Papers 2210.13843, arXiv.org, revised Jan 2024.
    2. Otsu, Taisuke & Takahata, Keisuke & Xu, Mengshan, 2023. "Empirical likelihood inference for monotone index model," LSE Research Online Documents on Economics 118123, London School of Economics and Political Science, LSE Library.
    3. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Mengshan Xu & Taisuke Otsu, 2022. "Isotonic propensity score matching," Papers 2207.08868, arXiv.org, revised Aug 2024.
    5. Fadoua Balabdaoui & Cécile Durot & Christopher Fragneau, 2021. "On the population least‐squares criterion in the monotone single index model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 408-436, November.
    6. Xu, Mengshan & Otsu, Taisuke, 2020. "Score estimation of monotone partially linear index model," LSE Research Online Documents on Economics 106698, London School of Economics and Political Science, LSE Library.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:46:y:2019:i:2:p:517-544. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.