Statistical clustering is a procedure of classifying a set of objects such that objects in the same class (called cluster) are more homogeneous, with respect to some features or characteristics of objects, to each other than to those in any other classes. In this paper, we apply four clustering approaches to improving forecasting performances of the Lee–Carter and CBD models. First, each of four clustering methods (Ward’s hierarchical clustering, divisive hierarchical clustering, K-means clustering, and Gaussian mixture model clustering) is adopted to determine, based on some characteristics of mortality rates, the number and partition of age clusters from the whole study ages 25-84. Next, we forecast 10-year and 20-year mortality rates for each of the age clusters using the Lee–Carter and CBD models, respectively. Finally, numerical illustrations are given with two R packages “NbClust” and “mclust” for clustering. Mortality data for both genders of the US and the UK are obtained from the Human Mortality Database, and the MAPE (mean absolute percentage error) measure is adopted to evaluate forecasting performance. Comparisons of MAPE values are made with and without clustering, which demonstrate that all the proposed clustering methods can improve forecasting performances of the Lee–Carter and CBD models.

统计聚类是对一组对象进行分类的过程，以使同一类（称为聚类）中的对象相对于对象的某些特征或特性，彼此之间的同质性高于其他任何类别的对象。在本文中，我们应用四种聚类方法来改善Lee-Carter模型和CBD模型的预测性能。首先，根据死亡率的某些特征，采用四种聚类方法（沃德层次聚类，分裂层次聚类，K均值聚类和高斯混合模型聚类）来确定年龄聚类的总数和划分研究年龄在25-84岁之间。接下来，我们分别使用Lee-Carter模型和CBD模型预测每个年龄段的10岁和20岁死亡率。最后，给出了两个R包“ NbClust”和“ mclust”进行聚类的数字插图。从人类死亡率数据库中获得了美国和英国的男女死亡率数据，并采用了MAPE（平均绝对百分比误差）度量来评估预测性能。比较有聚类和无聚类的MAPE值，这表明所有提出的聚类方法都可以改善Lee-Carter模型和CBD模型的预测性能。