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Averaging quantiles, variance shrinkage, and overconfidence

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  • Roger M. Cooke

Abstract

Averaging quantiles as a way of combining experts' judgments is studied both mathematically and empirically. Quantile averaging is equivalent to taking the harmonic mean of densities evaluated at quantile points. A variance shrinkage law is established between equal and harmonic weighting. Data from 49 post‐2006 studies are extended to include harmonic weighting in addition to equal and performance‐based weighting. It emerges that harmonic weighting has the highest average information and degraded statistical accuracy. The hypothesis that the quantile average is statistically accurate would be rejected at the 5% level in 28 studies and at the 0.1% level in 15 studies. For performance weighting, these numbers are 3 and 1, for equal weighting 2 and 1.

Suggested Citation

  • Roger M. Cooke, 2023. "Averaging quantiles, variance shrinkage, and overconfidence," Futures & Foresight Science, John Wiley & Sons, vol. 5(1), March.
    • Handle: RePEc:wly:fufsci:v:5:y:2023:i:1:n:e139
    DOI: 10.1002/ffo2.139
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    1. Cooke, Roger M. & Marti, Deniz & Mazzuchi, Thomas, 2021. "Expert forecasting with and without uncertainty quantification and weighting: What do the data say?," International Journal of Forecasting, Elsevier, vol. 37(1), pages 378-387.
    2. Michael Oppenheimer & Christopher M. Little & Roger M. Cooke, 2016. "Expert judgement and uncertainty quantification for climate change," Nature Climate Change, Nature, vol. 6(5), pages 445-451, May.
    3. Colson, Abigail R. & Cooke, Roger M., 2017. "Cross validation for the classical model of structured expert judgment," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 109-120.
    4. De Gooijer, Jan G. & Zerom, Dawit, 2019. "Semiparametric quantile averaging in the presence of high-dimensional predictors," International Journal of Forecasting, Elsevier, vol. 35(3), pages 891-909.
    5. Kenneth C. Lichtendahl & Yael Grushka-Cockayne & Robert L. Winkler, 2013. "Is It Better to Average Probabilities or Quantiles?," Management Science, INFORMS, vol. 59(7), pages 1594-1611, July.
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