多元评分规则区分能力的评价
Evaluating the Discrimination Ability of Proper Multivariate Scoring Rules
摘要：
通常采用适当的评分规则来量化分布预测的准确性。给定一个观察结果，他们为每个分布预测分配一个标量分数，最低的预期分数归因于真实分布。能量和变异函数分数是最近在多元设置中获得一些流行的两个规则，因为它们的计算不需要预测具有参数密度函数，因此它们具有广泛的适用性。在这里，我们进行了模拟研究，以比较之间的区别能力的能量分数和三个变异函数分数。与其他研究相比，我们的模拟设计更现实，因为它是由包含商品价格，货币和利率的历史数据集支持，我们的数据生成过程包括不同的边缘分布，依赖结构和校准窗口的模型的多样化选择。这有助于全面比较适当的评分规则在不同环境中的表现。为了比较分数，我们使用三个指标：平均相对分数，错误率和广义判别启发式。总的来说，我们发现参数p=0.5的变差函数得分优于能量得分和其他两个变差函数得分。
英文摘要：
Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalised discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5 outperforms the energy score and the other two variogram scores.
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