极端分位数的评分预测
Scoring Predictions at Extreme Quantiles
摘要：
极端尾部的分位数预测在许多应用中是令人感兴趣的。极值模型为这个点预测问题提供了各种相互竞争的预测因子。评估一组竞争预测因子的常用方法是评估它们在给定情况下的预测性能。然而，由于该推断问题的极端性质，可能在历史记录中看不到预测的分位数，特别是当样本量小时。这种情况给预测的验证及其实现带来了问题。在这篇文章中，我们提出了两个非参数评分方法来评估极端分位数预测机制。所提出的评估方法是基于预测一系列同样极端的分位数的不同部分的数据。然后，我们使用分位数评分函数来评估竞争预测因子。通过仿真研究，将该评分方法与传统评分方法进行了性能比较，证明了前者的优越性。然后，该方法被应用到重新分析网络从洛斯阿拉莫斯国家实验室和每日降水数据在加利福尼亚州的一个站，可从全球历史气候学网络的Netflow数据。
英文摘要：
Prediction of quantiles at extreme tails is of interest in numerous applications. Extreme value modelling provides various competing predictors for this point prediction problem. A common method of assessment of a set of competing predictors is to evaluate their predictive performance in a given situation. However, due to the extreme nature of this inference problem, it can be possible that the predicted quantiles are not seen in the historical records, particularly when the sample size is small. This situation poses a problem to the validation of the prediction with its realisation. In this article, we propose two non-parametric scoring approaches to assess extreme quantile prediction mechanisms. The proposed assessment methods are based on predicting a sequence of equally extreme quantiles on different parts of the data. We then use the quantile scoring function to evaluate the competing predictors. The performance of the scoring methods is compared with the conventional scoring method and the superiority of the former methods are demonstrated in a simulation study. The methods are then applied to reanalyse cyber Netflow data from Los Alamos National Laboratory and daily precipitation data at a station in California available from Global Historical Climatology Network.
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