多元预测评价：敏感性与严格适切性 评分规则

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摘要翻译：
近年来，概率预测是一个新兴的课题，因此越来越需要合适的方法来评价多元预测。我们分析了最常见的评分规则的敏感性，特别是关于预测的依赖结构的质量。另外，我们提出了基于copula的评分规则，它唯一地描述了具有连续边际分布的每个概率分布的依赖结构。讨论了所考虑的评分规则和评价方法的有效估计，如Diebold-Mariano检验。在详细的仿真研究中，我们比较了著名的评分规则和我们提出的评分规则的性能。除了基于最近发表的结果的扩展综合研究之外，我们还考虑了一个真实的数据例子。我们发现能量评分，这可能是最广泛使用的多元评分规则，在检测预测误差方面表现得相当好，也包括相关性。这与其他研究相矛盾。结果还表明，提出的copula评分在依赖结构正确和不正确的模型之间提供了非常强的区分。我们最后对拟议的方法进行全面讨论。
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英文标题：
《Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper
  Scoring Rules》
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作者：
Florian Ziel, Kevin Berk
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最新提交年份：
2019
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
--
一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Statistics        统计学
二级分类：Other Statistics        其他统计数字
分类描述：Work in statistics that does not fit into the other stat classifications
从事不适合其他统计分类的统计工作
--

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英文摘要：
  In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules, especially regarding quality of the forecasted dependency structures. Additionally, we propose scoring rules based on the copula, which uniquely describes the dependency structure for every probability distribution with continuous marginal distributions. Efficient estimation of the considered scoring rules and evaluation methods such as the Diebold-Mariano test are discussed. In detailed simulation studies, we compare the performance of the renowned scoring rules and the ones we propose. Besides extended synthetic studies based on recently published results we also consider a real data example. We find that the energy score, which is probably the most widely used multivariate scoring rule, performs comparably well in detecting forecast errors, also regarding dependencies. This contradicts other studies. The results also show that a proposed copula score provides very strong distinction between models with correct and incorrect dependency structure. We close with a comprehensive discussion on the proposed methodology.
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PDF链接：
https://arxiv.org/pdf/1910.07325

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关键词：敏感性 Multivariate econometrics distribution R statistics copula 结构 能量 具有 rules