The focus of the present paper is to forecast mortality rates for small sub-populations that are parts of a larger super-population. In this setting the assumption is that it is possible to produce reliable forecasts for the super-population, but the sub-populations may be too small or lack sufficient history to produce reliable forecasts if modelled separately. This setup is aligned with the ideas that underpin credibility theory, and in the present paper the classical credibility theory approach is extended to be able to handle the situation where future mortality rates are driven by a latent stochastic process, as is the case for, e.g., Lee-Carter type models. This results in sub-population credibility predictors that are weighted averages of expected future super-population mortality rates and expected future sub-population specific mortality rates. Due to the predictor's simple structure it is possible to derive an explicit expression for the expected quadratic forecast error. Moreover, the proposed credibility modelling approach does not depend on the specific form of the super-population model, making it broadly applicable regardless of the chosen forecasting model for the super-population. The performance of the suggested sub-population credibility predictor is illustrated on simulated population data. These illustrations highlight how the credibility predictor serves as a compromise between only using a super-population model, and only using a potentially unreliable sub-population specific model.

翻译：本文聚焦于预测隶属于更大总群体的小规模子群体的死亡率。在此设定下，假设能够为总群体生成可靠预测，但若单独建模，子群体可能因规模过小或历史数据不足而无法产生可靠预测。这一框架与信度理论的基本思想一致，本文将经典信度理论方法进行扩展，使其能够处理未来死亡率由潜在随机过程驱动的情况——例如Lee-Carter类模型。由此得到子群体信度预测器，其为总群体未来预期死亡率与子群体特定预期死亡率的加权平均。得益于预测器的简洁结构，可推导出期望二次预测误差的显式表达式。此外，所提出的信度建模方法不依赖于总群体模型的具体形式，因此无论选择何种总群体预测模型均具有广泛适用性。通过模拟人口数据展示了建议的子群体信度预测器的性能。这些案例突显了信度预测器如何作为一种折衷方案，兼顾仅使用总群体模型与仅使用潜在不可靠的子群体特定模型两种极端情况。