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The mode functional is not elicitable

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  • C. Heinrich

Abstract

This article is concerned with point forecasting of a real-valued random variable with a general Lebesgue density. Answering a question of Gneiting (2011), it is shown that the mode is not elicitable, or, in other words, that it is impossible to find a loss or scoring function under which the mode is the Bayes predictor.

Suggested Citation

  • C. Heinrich, 2014. "The mode functional is not elicitable," Biometrika, Biometrika Trust, vol. 101(1), pages 245-251.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:245-251.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast048
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    Cited by:

    1. Fissler, Tobias & Pesenti, Silvana M., 2023. "Sensitivity measures based on scoring functions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1408-1423.
    2. Ruodu Wang & Yunran Wei, 2020. "Risk functionals with convex level sets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1337-1367, October.
    3. Patrick Schmidt & Matthias Katzfuss & Tilmann Gneiting, 2021. "Interpretation of point forecasts with unknown directive," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 728-743, September.
    4. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    5. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    6. Tobias Fissler & Johanna F. Ziegel, 2019. "Evaluating Range Value at Risk Forecasts," Papers 1902.04489, arXiv.org, revised Nov 2020.
    7. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    8. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jun 2023.
    9. Hajo Holzmann & Matthias Eulert, 2014. "The role of the information set for forecasting - with applications to risk management," Papers 1404.7653, arXiv.org.
    10. Tobias Fissler & Jana Hlavinov'a & Birgit Rudloff, 2019. "Elicitability and Identifiability of Systemic Risk Measures," Papers 1907.01306, arXiv.org, revised Oct 2019.
    11. Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.
    12. Krisztina Dearborn & Rafael Frongillo, 2020. "On the indirect elicitability of the mode and modal interval," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1095-1108, October.

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