论文标题
我们可以从死亡率数据的功能聚类中学到什么？ HMD数据的应用程序
What can we learn from functional clustering of mortality data? An application to HMD data
论文作者
论文摘要
在大多数情况下，考虑摘要指标（例如$ g。$ e_0 $或$ e^{\ dagger} _0 $），对死亡率进行分析，该指标要么集中在特定的死亡率组件上，要么以一个度量为单位。当我们有兴趣分析死亡模式的全球演变而不忽视特定组成部分的演变时，这可能是一个限制。本文分析了发达国家的死亡率下降模式是否存在不同的模式，从而确定了所有死亡率组成部分的作用。我们使用功能数据分析（FDA）方法实施集群分析，这使我们可以考虑特定年龄的死亡率，而不是分析曲线而不是标量数据时的摘要措施。结合功能性主成分分析（PCA）方法，它可以识别曲线的哪个部分（死亡率组件）负责将一个国家分配给特定集群。 FDA聚类应用于32个人类死亡率数据库和1960 - 2010年。结果表明，发达国家的演变遵循相同的模式（有不同的时机）：（1）降低婴儿死亡率，（2）过早死亡率的增加，（3）死亡的转移和压缩。一些国家正在遵循该计划，并用前体恢复差距，而另一些则没有显示出恢复的迹象。东欧国家仍处于阶段（2），目前尚不清楚是否以及何时进入阶段（3）。该国的所有差异都与各国经历集群确定的阶段的不同时机有关。因此，基于FDA的聚类分析允许对被考虑的国家的死亡率下降模式进行全面的了解。
In most cases, mortality is analysed considering summary indicators (e.~g. $e_0$ or $e^{\dagger}_0$) that either focus on a specific mortality component or pool all component-specific information in one measure. This can be a limitation, when we are interested to analyse the global evolution of mortality patterns without loosing sight of specific components evolution. The paper analyses whether there are different patterns of mortality decline among developed countries, identifying the role played by all the mortality components. We implement a cluster analysis using a Functional Data Analysis (FDA) approach, which allows us to consider age-specific mortality rather than summary measures as it analyses curves rather than scalar data. Combined with a Functional Principal Component Analysis (PCA) method it can identify what part of the curves (mortality components) is responsible for assigning one country to a specific cluster. FDA clustering is applied to 32 countries of Human Mortality Database and years 1960--2010. The results show that the evolutions of developed countries follow the same pattern (with different timing): (1) a reduction of infant mortality, (2) an increase of premature mortality, (3) a shift and compression of deaths. Some countries are following this scheme and recovering the gap with precursors, others do not show signs of recovery. Eastern Europe countries are still at stage (2) and it is not clear if and when they will enter into phase (3). All the country differences relates the different timing with which countries undergo the stages identified by clusters. The cluster analysis based on FDA allows therefore a comprehensive understanding of the patterns of mortality decline for considered countries.
