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On the indirect elicitability of the mode and modal interval

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  • Krisztina Dearborn

    (University of Colorado Boulder)

  • Rafael Frongillo

    (University of Colorado Boulder)

Abstract

Scoring functions are commonly used to evaluate a point forecast of a particular statistical functional. This scoring function should be consistent, meaning the correct value of the functional is the Bayes act, in which case we say the scoring function elicits the functional. Recent results show that the mode functional is not elicitable. In this work, we ask whether it is at least possible to indirectly elicit the mode, wherein one elicits a low-dimensional functional from which the mode can be computed. We show that this cannot be done: Neither the mode nor a modal interval is indirectly elicitable with respect to the class of identifiable functionals.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:5:d:10.1007_s10463-019-00719-1
    DOI: 10.1007/s10463-019-00719-1
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    References listed on IDEAS

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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    3. C. Heinrich, 2014. "The mode functional is not elicitable," Biometrika, Biometrika Trust, vol. 101(1), pages 245-251.
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    Cited by:

    1. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jul 2024.

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