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Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings

Citations

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Cited by:

  1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
  2. Cathy W. S. Chen & Takaaki Koike & Wei‐Hsuan Shau, 2024. "Tail risk forecasting with semiparametric regression models by incorporating overnight information," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1492-1512, August.
  3. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
  4. Taillardat, Maxime & Fougères, Anne-Laure & Naveau, Philippe & de Fondeville, Raphaël, 2023. "Evaluating probabilistic forecasts of extremes using continuous ranked probability score distributions," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1448-1459.
  5. Tobias Fissler & Yannick Hoga, 2021. "Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability," Papers 2104.10673, arXiv.org, revised Feb 2022.
  6. Martin, Gael M. & Loaiza-Maya, Rubén & Maneesoonthorn, Worapree & Frazier, David T. & Ramírez-Hassan, Andrés, 2022. "Optimal probabilistic forecasts: When do they work?," International Journal of Forecasting, Elsevier, vol. 38(1), pages 384-406.
  7. Julia Mortera & A. Philip Dawid, 2017. "A Note on Prediction Markets," Departmental Working Papers of Economics - University 'Roma Tre' 0215, Department of Economics - University Roma Tre.
  8. Taylor, James W., 2020. "Forecast combinations for value at risk and expected shortfall," International Journal of Forecasting, Elsevier, vol. 36(2), pages 428-441.
  9. Chen, Yi-Ting & Liu, Chu-An & Su, Jiun-Hua, 2025. "Bregman model averaging for forecast combination," Journal of Econometrics, Elsevier, vol. 251(C).
  10. Sander Barendse & Andrew J. Patton, 2022. "Comparing Predictive Accuracy in the Presence of a Loss Function Shape Parameter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1057-1069, June.
  11. Miao, Kathleen E. & Pesenti, Silvana M., 2025. "Robust elicitable functionals," European Journal of Operational Research, Elsevier, vol. 326(2), pages 311-325.
  12. Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
  13. Ruben Loaiza‐Maya & Gael M. Martin & David T. Frazier, 2021. "Focused Bayesian prediction," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 517-543, August.
  14. Guy P. Nason & James L. Wei, 2022. "Quantifying the economic response to COVID‐19 mitigations and death rates via forecasting purchasing managers' indices using generalised network autoregressive models with exogenous variables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1778-1792, October.
  15. Krüger, Fabian & Pavlova, Lora, 2019. "Quantifying subjective oncertainty in survey expectations," Working Papers 0664, University of Heidelberg, Department of Economics.
  16. Xenxo Vidal-Llana & Carlos Salort Sánchez & Vincenzo Coia & Montserrat Guillen, 2022. ""Non-Crossing Dual Neural Network: Joint Value at Risk and Conditional Tail Expectation estimations with non-crossing conditions"," IREA Working Papers 202215, University of Barcelona, Research Institute of Applied Economics, revised Oct 2022.
  17. Cathy W. S. Chen & Cindy T. H. Chien, 2024. "Improving Quantile Forecasts via Realized Double Hysteretic GARCH Model in Stock Markets," Computational Economics, Springer;Society for Computational Economics, vol. 64(6), pages 3447-3471, December.
  18. Borgonovo, Emanuele & Jose, Victor Richmond R. & Knowlton, Morgan & Shachter, Ross & Siebert, Johannes Ulrich & Ulu, Canan, 2026. "Fifty years of decision analysis in operational research: A review," European Journal of Operational Research, Elsevier, vol. 329(2), pages 355-377.
  19. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.
  20. Fissler, Tobias & Pesenti, Silvana M., 2023. "Sensitivity measures based on scoring functions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1408-1423.
  21. Adam Maidman & Lan Wang, 2018. "New semiparametric method for predicting high‐cost patients," Biometrics, The International Biometric Society, vol. 74(3), pages 1104-1111, September.
  22. Denuit, Michel & Huyghe, Julie & Trufin, Julien & Verdebout, Thomas, 2024. "Testing for auto-calibration with Lorenz and Concentration curves," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 130-139.
  23. Arian, Hamid & Moghimi, Mehrdad & Tabatabaei, Ehsan & Zamani, Shiva, 2022. "Encoded Value-at-Risk: A machine learning approach for portfolio risk measurement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 500-525.
  24. Malte Knüppel & Fabian Krüger, 2022. "Forecast uncertainty, disagreement, and the linear pool," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 23-41, January.
  25. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
  26. Jonas R. Brehmer & Tilmann Gneiting & Marcus Herrmann & Warner Marzocchi & Martin Schlather & Kirstin Strokorb, 2024. "Comparative evaluation of point process forecasts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 47-71, February.
  27. Yuru Sun & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Gael M. Martin, 2023. "Optimal probabilistic forecasts for risk management," Papers 2303.01651, arXiv.org.
  28. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).
  29. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.
  30. Anubha Goel & Puneet Pasricha & Juho Kanniainen, 2024. "Time-Series Foundation AI Model for Value-at-Risk Forecasting," Papers 2410.11773, arXiv.org, revised May 2025.
  31. Fabio Bellini & Ilia Negri & Mariya Pyatkova, 2019. "Backtesting VaR and expectiles with realized scores," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 119-142, March.
  32. Tobias Fissler & Jana Hlavinov'a & Birgit Rudloff, 2019. "Elicitability and Identifiability of Systemic Risk Measures," Papers 1907.01306, arXiv.org, revised Oct 2019.
  33. Shovon Sengupta & Sunny Kumar Singh & Tanujit Chakraborty, 2025. "Macroeconomic Forecasting for the G7 countries under Uncertainty Shocks," Papers 2510.23347, arXiv.org.
  34. Alexander Henzi & Johanna F. Ziegel & Tilmann Gneiting, 2021. "Isotonic distributional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 963-993, November.
  35. Daniel Ober-Reynolds, 2023. "Estimating Functionals of the Joint Distribution of Potential Outcomes with Optimal Transport," Papers 2311.09435, arXiv.org.
  36. 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.
  37. Fritzsch, Simon & Timphus, Maike & Weiß, Gregor, 2024. "Marginals versus copulas: Which account for more model risk in multivariate risk forecasting?," Journal of Banking & Finance, Elsevier, vol. 158(C).
  38. Castiglione, Cristian & Arnone, Eleonora & Bernardi, Mauro & Farcomeni, Alessio & Sangalli, Laura M., 2025. "PDE-regularised spatial quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 205(C).
  39. Kathleen E. Miao & Silvana M. Pesenti, 2024. "Robust Elicitable Functionals," Papers 2409.04412, arXiv.org, revised Feb 2025.
  40. Wang, Shuai & Wang, Qian & Lu, Helen & Zhang, Dongxue & Xing, Qianyi & Wang, Jianzhou, 2025. "Learning about tail risk: Machine learning and combination with regularization in market risk management," Omega, Elsevier, vol. 133(C).
  41. Ibrahim M. Almanjahie & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2024. "The local linear functional kNN estimator of the conditional expectile: uniform consistency in number of neighbors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 1007-1035, November.
  42. Jonas R. Brehmer & Tilmann Gneiting, 2020. "Properization: constructing proper scoring rules via Bayes acts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 659-673, June.
  43. Timothy I. Cannings & Richard J. Samworth, 2017. "Random-projection ensemble classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 959-1035, September.
  44. Donia Besher & Anirban Sengupta & Tanujit Chakraborty, 2025. "Probabilistic Forecasting of Climate Policy Uncertainty: The Role of Macro-financial Variables and Google Search Data," Papers 2507.12276, arXiv.org, revised Jan 2026.
  45. Krüger, Fabian & Pavlova, Lora, 2024. "Quantifying subjective uncertainty in survey expectations," International Journal of Forecasting, Elsevier, vol. 40(2), pages 796-810.
  46. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2022. "Characterizing M-estimators," Papers 2208.08108, arXiv.org.
  47. Marc-Oliver Pohle, 2020. "The Murphy Decomposition and the Calibration-Resolution Principle: A New Perspective on Forecast Evaluation," Papers 2005.01835, arXiv.org.
  48. Tanujit Chakraborty & Donia Besher & Madhurima Panja & Shovon Sengupta, 2025. "Neural ARFIMA model for forecasting BRIC exchange rates with long memory under oil shocks and policy uncertainties," Papers 2509.06697, arXiv.org.
  49. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
  50. Dimitriadis, Timo & Gneiting, Tilmann & Jordan, Alexander I. & Vogel, Peter, 2024. "Evaluating probabilistic classifiers: The triptych," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1101-1122.
  51. Lieli, Robert P. & Stinchcombe, Maxwell B. & Grolmusz, Viola M., 2019. "Unrestricted and controlled identification of loss functions: Possibility and impossibility results," International Journal of Forecasting, Elsevier, vol. 35(3), pages 878-890.
  52. Xiaochun Meng & James W. Taylor & Souhaib Ben Taieb & Siran Li, 2020. "Scores for Multivariate Distributions and Level Sets," Papers 2002.09578, arXiv.org, revised Jun 2023.
  53. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  54. Koike, Takaaki & Chen, Cathy W.S. & Lin, Edward M.H., 2025. "Forecasting and backtesting gradient allocations of expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 124(C).
  55. Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose & Robert L. Winkler, 2017. "Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs," Operations Research, INFORMS, vol. 65(3), pages 712-728, June.
  56. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
  57. Abbas, Yasser & Daouia, Abdelaati & Nemouchi, Boutheina & Stupfler, Gilles, 2025. "Tail expectile-VaR estimation in the semiparametric Generalized Pareto model," TSE Working Papers 25-1607, Toulouse School of Economics (TSE).
  58. Ziegel, Johanna F. & Krueger, Fabian & Jordan, Alexander & Fasciati, Fernando, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Working Papers 0632, University of Heidelberg, Department of Economics.
  59. Tobias Fissler & Johanna F. Ziegel, 2019. "Evaluating Range Value at Risk Forecasts," Papers 1902.04489, arXiv.org, revised Nov 2020.
  60. Johanna F. Ziegel & Fabian Kruger & Alexander Jordan & Fernando Fasciati, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Papers 1705.04537, arXiv.org.
  61. Alexander Henzi & Johanna F Ziegel, 2022. "Valid sequential inference on probability forecast performance [A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems]," Biometrika, Biometrika Trust, vol. 109(3), pages 647-663.
  62. Mucahit Aygun & Fabio Bellini & Roger J. A. Laeven, 2023. "Elicitability of Return Risk Measures," Papers 2302.13070, arXiv.org, revised Mar 2023.
  63. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
  64. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
  65. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2021. "ExpectHill estimation, extreme risk and heavy tails," Journal of Econometrics, Elsevier, vol. 221(1), pages 97-117.
  66. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.
  67. Yen, Yu-Min & Yen, Tso-Jung, 2021. "Testing forecast accuracy of expectiles and quantiles with the extremal consistent loss functions," International Journal of Forecasting, Elsevier, vol. 37(2), pages 733-758.
  68. Drachal, Krzysztof, 2021. "Forecasting crude oil real prices with averaging time-varying VAR models," Resources Policy, Elsevier, vol. 74(C).
  69. Qinyu Wu & Fan Yang & Ping Zhang, 2023. "Conditional generalized quantiles based on expected utility model and equivalent characterization of properties," Papers 2301.12420, arXiv.org.
  70. Alexander I. Jordan & Anja Mühlemann & Johanna F. Ziegel, 2022. "Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 489-514, June.
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