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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.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa093
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    Citations

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    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. Christis Katsouris, 2023. "Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models," Papers 2311.08218, arXiv.org, revised Dec 2023.
    3. Tobias Fissler & Michael Merz & Mario V. Wuthrich, 2021. "Deep Quantile and Deep Composite Model Regression," Papers 2112.03075, arXiv.org.
    4. 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.
    5. Qiuqi Wang & Ruodu Wang & Johanna Ziegel, 2022. "E-backtesting," Papers 2209.00991, arXiv.org, revised May 2023.

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