AI 中文总结
针对受随机右删失的非同分布极端观测值，提出 Beran 型相对事件 scedasis 估计量，通过扩展生存分析理论推导其一致性，经模拟和保险索赔应用验证了方法有效性。
AI 中文摘要
我们研究受随机右删失影响的非同分布极端观测值的尾部异质性估计。在无删失场景下，此类异质性由事件 scedasis 函数描述，该函数衡量不同设计点对上部尾部的相对贡献。然而在删失情况下，观测到的尾部异质性会被删失 scedasis 函数污染，应用无删失技术会针对错误对象。我们提出一种相对事件 scedasis 的 Beran 型估计量，其在温和条件下具有一致性。为得到这些结果，我们将上部次序统计量的生存分析表示扩展至非同分布情形；具体而言，我们在递增区间上发展了条件 Nelson–Aalen 和 Beran 理论，这些区间的随机端点以概率趋近于1被确定性高局部分位数主导。特别地，我们推导了条件 Nelson–Aalen 估计量的鞅阵列表示，其显式误差界仅取决于样本比例和带宽。模拟结果展示了该方法的有限样本性能，将其应用于法国财产意外伤害保险索赔案例则说明，异质性删失会如何扭曲朴素的 scedasis 估计量。
英文摘要
We study estimation of tail heterogeneity for non-identically distributed extreme observations subject to random right-censoring. In the uncensored setting, such heterogeneity is described by the event scedasis function, which measures the relative contribution of different design points to the upper tail. Under censoring, however, the observed tail heterogeneity is contaminated by the censoring scedasis functions, and applying uncensored techniques targets the wrong object. We propose a Beran-type estimator of the relative event scedasis, which is consistent under mild conditions. To obtain these results, survival analysis representations at an upper order statistics are extended to the non-identically distributed case; specifically, we develop conditional Nelson--Aalen and Beran theory on increasing intervals whose random endpoint is dominated, with probability tending to one, by a deterministic high local quantile. In particular, we derive a martingale array representation of the conditional Nelson--Aalen estimator with explicit error bounds depending only on the sample fraction and the bandwidth. Simulations demonstrate the finite-sample performance of the method, and an application to French property-casualty insurance claims illustrates how heterogeneous censoring can distort naive scedasis estimates.
