Lam Ka Kin, Wang Bo
School of Mathematics and Actuarial Science, University of Leicester, Leicester, UK.
J Appl Stat. 2022 Aug 3;50(15):3177-3198. doi: 10.1080/02664763.2022.2104228. eCollection 2023.
Human mortality patterns and trajectories in closely related populations are likely linked together and share similarities. It is always desirable to model them simultaneously while taking their heterogeneity into account. This article introduces two new models for joint mortality modelling and forecasting multiple subpopulations using the multivariate functional principal component analysis techniques. The first model extends the independent functional data model to a multipopulation modelling setting. In the second one, we propose a novel multivariate functional principal component method for coherent modelling. Its design primarily fulfils the idea that when several subpopulation groups have similar socio-economic conditions or common biological characteristics such close connections are expected to evolve in a non-diverging fashion. We demonstrate the proposed methods by using sex-specific mortality data. Their forecast performances are further compared with several existing models, including the independent functional data model and the Product-Ratio model, through comparisons with mortality data of ten developed countries. The numerical examples show that the first proposed model maintains a comparable forecast ability with the existing methods. In contrast, the second proposed model outperforms the first model as well as the existing models in terms of forecast accuracy.
密切相关人群的人类死亡率模式和轨迹可能相互关联并具有相似性。在考虑其异质性的同时对它们进行同步建模总是很有必要的。本文介绍了两种新的联合死亡率建模和预测多个亚人群的模型，使用多元函数主成分分析技术。第一个模型将独立函数数据模型扩展到多人群建模设置。在第二个模型中，我们提出了一种用于连贯建模的新型多元函数主成分方法。其设计主要实现了这样一种理念，即当几个亚人群组具有相似的社会经济条件或共同的生物学特征时，预计这种紧密联系将以非发散的方式演变。我们通过使用按性别分类的死亡率数据来演示所提出的方法。通过与十个发达国家的死亡率数据进行比较，进一步将它们的预测性能与几个现有模型进行比较，包括独立函数数据模型和乘积比模型。数值示例表明，第一个提出的模型与现有方法保持了相当的预测能力。相比之下，第二个提出的模型在预测准确性方面优于第一个模型以及现有模型。
