In this paper, we consider robust estimation of claim severity models in insurance, when data are affected by truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance). In particular, robust estimators based on the methods of trimmed moments (T-estimators) and winsorized moments (W-estimators) are pursued and fully developed. The general definitions of such estimators are formulated and their asymptotic properties are investigated. For illustrative purposes, specific formulas for T- and W-estimators of the tail parameter of a single-parameter Pareto distribution are derived. The practical performance of these estimators is then explored using the well-known Norwegian fire claims data. Our results demonstrate that T- and W-estimators offer a robust and computationally efficient alternative to the likelihood-based inference for models that are affected by deductibles, policy limits, and coinsurance.

翻译：本文研究了在数据受截断（因免赔额）、删失（因保单限额）和缩放（因共同保险）影响时，保险索赔严重程度模型的稳健估计问题。具体而言，我们基于修剪矩法（T-估计量）和缩尾矩法（W-估计量）提出并完整发展了稳健估计量。给出了此类估计量的一般定义，并研究了其渐近性质。为便于说明，推导了单参数Pareto分布尾部参数的T-估计量和W-估计量的具体公式。随后利用著名的挪威火灾索赔数据探索了这些估计量的实际表现。结果表明，对于受免赔额、保单限额和共同保险影响的模型，T-估计量和W-估计量提供了比基于似然的推断更稳健且计算高效的替代方案。