التفاصيل البيبلوغرافية
| العنوان: |
Scores for Multivariate Distributions and Level Sets. |
| المؤلفون: |
Meng, Xiaochun1 (AUTHOR) xiaochun.meng@sussex.ac.uk, Taylor, James W.2 (AUTHOR) james.taylor@sbs.ox.ac.uk, Ben Taieb, Souhaib3 (AUTHOR) souhaib.bentaieb@umons.ac.be, Li, Siran4 (AUTHOR) sl4025@nyu.edu |
| المصدر: |
Operations Research. Jan/Feb2025, Vol. 73 Issue 1, p344-362. 19p. |
| مصطلحات موضوعية: |
*DISTRIBUTION (Probability theory), *ECONOMIC forecasting, *DECISION making, *VALUE at risk, SET functions |
| مستخلص: |
Evaluating Forecasts of Multivariate Probability Distributions Forecasts of multivariate probability distributions are required for a variety of applications. The availability of a score for a forecast is important for evaluating prediction accuracy, as well as estimating model parameters. In "Scores for Multivariate Distributions and Level Sets," X. Meng, J. W. Taylor, S. Ben Taieb, and S. Li propose a theoretical framework that encompasses several existing scores for multivariate distributions and can be used to generate new scores. In some multivariate contexts, a forecast of a level set is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution, which can be used as a measure of risk. This motivates consideration of scores for level sets. The authors show that such scores can be obtained by decomposing the scores developed for multivariate distributions. A simple numerical algorithm is presented to compute the scores, and practical applications are provided in the contexts of conditional value-at-risk for financial data and the combination of expert macroeconomic forecasts. Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions that encompasses the existing quadratic score and multivariate continuous ranked probability score. We demonstrate how this framework can be used to generate new scoring rules. In some multivariate contexts, it is a forecast of a level set that is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution as a measure of risk. This motivates consideration of scoring functions for such level sets. For univariate distributions, it is well established that the continuous ranked probability score can be expressed as the integral over a quantile score. We show that, in a similar way, scoring rules for multivariate distributions can be decomposed to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level sets, including density level sets and level sets for cumulative distributions. To compute the scores, we propose a simple numerical algorithm. We perform a simulation study to support our proposals, and we use real data to illustrate usefulness for forecast combining and conditional value at risk estimation. Funding: The work of S. Li was supported by the National Natural Science Foundation of China [Grant 12201399] and the Shanghai Frontier Research Institute for Modern Analysis. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Business Source Index |