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Evaluating Quantile Assessments

Author

Listed:
  • Victor Richmond R. Jose

    (McDonough School of Business, Georgetown University, Washington, DC 20057)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

Quantile assessments are commonly encountered in the elicitation of probability distributions in decision analysis, forecasting, and risk analysis. Scoring rules have been developed to provide ex ante incentives for careful and truthful assessments and ex post evaluation measures in the context of probability assessment. We show that these scoring rules designed for probability assessment provide inappropriate incentives if used for quantile assessment. We investigate the properties of a linear family of scoring rules that are intended specifically for quantile assessment (including the assessment of multiple quantiles) and can be related to a realistic decision-making problem. These rules provide proper incentives for quantile assessment and yield higher expected scores for distributions that are more informative in the sense of having less dispersion. We discuss the special case of interval forecasts and a generalization involving transformations, and we briefly mention other possible extensions.

Suggested Citation

  • Victor Richmond R. Jose & Robert L. Winkler, 2009. "Evaluating Quantile Assessments," Operations Research, INFORMS, vol. 57(5), pages 1287-1297, October.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:5:p:1287-1297
    DOI: 10.1287/opre.1080.0665
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    References listed on IDEAS

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    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. Kenneth C. Lichtendahl, Jr. & Robert L. Winkler, 2007. "Probability Elicitation, Scoring Rules, and Competition Among Forecasters," Management Science, INFORMS, vol. 53(11), pages 1745-1755, November.
    3. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    4. Hora, Stephen C. & Hora, Judith A. & Dodd, Nancy G., 1992. "Assessment of probability distributions for continuous random variables: A comparison of the bisection and fixed value methods," Organizational Behavior and Human Decision Processes, Elsevier, vol. 51(1), pages 133-155, February.
    5. Allan H. Murphy & Robert L. Winkler, 1977. "Reliability of Subjective Probability Forecasts of Precipitation and Temperature," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 41-47, March.
    6. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    7. R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 1-60, June.
    8. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    9. David V. Budescu & Ning Du, 2007. "Coherence and Consistency of Investors' Probability Judgments," Management Science, INFORMS, vol. 53(11), pages 1731-1744, November.
    10. Carl S. Spetzler & Carl-Axel S. Staël Von Holstein, 1975. "Exceptional Paper--Probability Encoding in Decision Analysis," Management Science, INFORMS, vol. 22(3), pages 340-358, November.
    11. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2008. "Scoring Rules, Generalized Entropy, and Utility Maximization," Operations Research, INFORMS, vol. 56(5), pages 1146-1157, October.
    12. 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.
    13. Robert L. Winkler, 1994. "Evaluating Probabilities: Asymmetric Scoring Rules," Management Science, INFORMS, vol. 40(11), pages 1395-1405, November.
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