IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v38y2019i9p979-1006.html
   My bibliography  Save this article

A practical guide to compact infinite dimensional parameter spaces

Author

Listed:
  • Joachim Freyberger
  • Matthew A. Masten

Abstract

Compactness is a widely used assumption in econometrics. In this article, we gather and review general compactness results for many commonly used parameter spaces in nonparametric estimation, and we provide several new results. We consider three kinds of functions: (1) functions with bounded domains which satisfy standard norm bounds, (2) functions with bounded domains which do not satisfy standard norm bounds, and (3) functions with unbounded domains. In all three cases, we provide two kinds of results, compact embedding and closedness, which together allow one to show that parameter spaces defined by a ||·||s-norm bound are compact under a norm ||·||c. We illustrate how the choice of norms affects the parameter space, the strength of the conclusions, as well as other regularity conditions in two common settings: nonparametric mean regression and nonparametric instrumental variables estimation.

Suggested Citation

  • Joachim Freyberger & Matthew A. Masten, 2019. "A practical guide to compact infinite dimensional parameter spaces," Econometric Reviews, Taylor & Francis Journals, vol. 38(9), pages 979-1006, October.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:9:p:979-1006
    DOI: 10.1080/07474938.2018.1514025
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2018.1514025
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2018.1514025?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.

    Citations

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


    Cited by:

    1. Jun, Sung Jae & Zincenko, Federico, 2022. "Testing for risk aversion in first-price sealed-bid auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 295-320.
    2. Dalderop, Jeroen, 2023. "Semiparametric estimation of latent variable asset pricing models," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    4. Ben Deaner, 2019. "Nonparametric Instrumental Variables Estimation Under Misspecification," Papers 1901.01241, arXiv.org, revised Dec 2022.
    5. An, Yonghong & Hong, Shengjie & Zhang, Daiqiang, 2023. "A structural analysis of simple contracts," Journal of Econometrics, Elsevier, vol. 236(2).
    6. Isaac Loh, 2024. "Inference under partial identification with minimax test statistics," Papers 2401.13057, arXiv.org, revised Apr 2024.
    7. Fan, Yanqin & Shi, Xuetao & Tao, Jing, 2023. "Partial identification and inference in moment models with incomplete data," Journal of Econometrics, Elsevier, vol. 235(2), pages 418-443.
    8. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.

    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:taf:emetrv:v:38:y:2019:i:9:p:979-1006. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.