指数族PCA的保险组合数据回归
Compositional Data Regression in Insurance with Exponential Family PCA
摘要：
成分数据是只携带成分之间的相对信息的多变量观测。应用标准的多元统计方法学直接分析成分数据可能会导致悖论和误解。组合数据也经常出现在保险中，特别是远程信息处理信息。然而，这种类型的数据并没有得到应有的特殊待遇，在大多数现有的精算文献。在本文中，我们探索和研究使用指数族主成分分析（EPCA）来分析保险中的成分数据。该方法被应用于分析从美国矿山安全与健康管理局获得的数据集。数值结果表明，EPCA能够产生具有显著预测意义的主成分，提高了回归模型的预测精度。EPCA方法可以为精算师分析成分数据提供一个很有前途的有用工具。
英文摘要：
Compositional data are multivariate observations that carry only relative information between components. Applying standard multivariate statistical methodology directly to analyze compositional data can lead to paradoxes and misinterpretations. Compositional data also frequently appear in insurance, especially with telematics information. However, such type of data does not receive deserved special treatment in most existing actuarial literature. In this paper, we explore and investigate the use of exponential family principal component analysis (EPCA) to analyze compositional data in insurance. The method is applied to analyze a dataset obtained from the U.S. Mine Safety and Health Administration. The numerical results show that EPCA is able to produce principal components that are significant predictors and improve the prediction accuracy of the regression model. The EPCA method can be a promising useful tool for actuaries to analyze compositional data.
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