IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v108y2021i4p857-879..html
   My bibliography  Save this article

Elicitation complexity of statistical properties
[A characterization of scoring rules for linear properties]

Author

Listed:
  • Rafael M Frongillo
  • Ian A Kash

Abstract

SummaryA property, or statistical functional, is said to be elicitable if it minimizes the expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work has sought to identify which properties are elicitable, here we investigate a more nuanced question: how many dimensions are required to indirectly elicit a given property? This number is called the elicitation complexity of the property. We lay the foundation for a general theory of elicitation complexity, which includes several basic results on how elicitation complexity behaves and the complexity of standard properties of interest. Building on this foundation, our main result gives tight complexity bounds for the broad class of Bayes risks. We apply these results to several properties of interest, including variance, entropy, norms and several classes of financial risk measures. The article concludes with a discussion and open questions.

Suggested Citation

  • Rafael M Frongillo & Ian A Kash, 2021. "Elicitation complexity of statistical properties [A characterization of scoring rules for linear properties]," Biometrika, Biometrika Trust, vol. 108(4), pages 857-879.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:4:p:857-879.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asaa093
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Fissler, Tobias & Merz, Michael & Wüthrich, Mario V., 2023. "Deep quantile and deep composite triplet regression," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 94-112.
    2. Fabio Bellini & Tiantian Mao & Ruodu Wang & Qinyu Wu, 2024. "Disappointment concordance and duet expectiles," Papers 2404.17751, arXiv.org, revised Oct 2024.
    3. Christis Katsouris, 2023. "Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models," Papers 2311.08218, arXiv.org, revised Apr 2024.
    4. Tobias Fissler & Michael Merz & Mario V. Wuthrich, 2021. "Deep Quantile and Deep Composite Model Regression," Papers 2112.03075, arXiv.org.
    5. Paul Embrechts & Tiantian Mao & Qiuqi Wang & Ruodu Wang, 2021. "Bayes risk, elicitability, and the Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1190-1217, October.
    6. Tobias Fissler & Fangda Liu & Ruodu Wang & Linxiao Wei, 2024. "Elicitability and identifiability of tail risk measures," Papers 2404.14136, arXiv.org, revised Jun 2024.
    7. Qiuqi Wang & Ruodu Wang & Johanna Ziegel, 2022. "E-backtesting," Papers 2209.00991, arXiv.org, revised Aug 2024.

    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:oup:biomet:v:108:y:2021:i:4:p:857-879.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.