纵向精算数据建模前的诊断检验
Diagnostic Tests Before Modeling Longitudinal Actuarial Data
AI总结：
针对非寿险纵向精算数据建模前的序列动态与依赖结构假设验证空白，提出序列动态检验与相关性检验两种诊断方法，经模拟和真实数据集验证有效，可为建模提供方向依据。
摘要：
在非寿险领域，使用纵向保险数据前理解其序列动态与依赖结构至关重要。现有精算文献主要聚焦建模，通常假设多年间索赔无序列动态且依赖结构预先设定。为填补这一研究空白，我们提出两种诊断检验，即序列动态检验与相关性检验，用于评估上述假设的合理性并提供有据可依的建模方向。检验包含以下要素：i）计算逻辑回归模型下截面估计参数的变化量，以及索赔发生指示变量跨时间的经验残差相关性，将其作为检测序列动态的指标；ii）采用随机加权bootstrap方法量化估计不确定性；iii）构建渐近理论以确立合适的检验统计量。通过模拟数据对所提检验进行验证，并将其应用于两个非寿险数据集，结果显示两个数据集的表现存在差异。
英文摘要：
In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of the cross-sectional estimated parameters under a logistic regression model and the empirical residual correlations of the claim occurrence indicators across time, which serve as the indications to detect serial dynamics; ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach; iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently.
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