Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from cause-specific mortality rates. In this work, we develop a novel functional concurrent regression model in which independent variables are functional compositions. This allows us to investigate the relationship over time between life expectancy at birth and compositions derived from cause-specific mortality rates of four distinct age classes, namely 0--4, 5--39, 40--64 and 65+. A penalized approach is developed to estimate the regression coefficients and select the relevant variables. Then an efficient computational strategy based on an augmented Lagrangian algorithm is derived to solve the resulting optimization problem. The good performances of the model in predicting the response function and estimating the unknown functional coefficients are shown in a simulation study. The results on real data confirm the important role of neoplasms and cardiovascular diseases in determining life expectancy emerged in other studies and reveal several other contributions not yet observed.
翻译:作为跨部门构成数据的多变量功能数据正在引起对统计模型文献的兴趣,一个主要实例是,从特定原因死亡率得出的构成构成过程中的轨迹。在这项工作中,我们开发了一个新的功能并行回归模型,独立变量是功能构成。这使我们能够调查出生时预期寿命与四个不同年龄类别(即0-4、5-39、40-64和65+)特定原因死亡率的构成之间的关系。制定了一种惩罚性办法,以估计回归系数和选择相关变量。然后根据拉格朗日算法制定高效的计算战略,以解决由此产生的优化问题。模型在预测反应函数和估计未知功能系数方面的良好表现在模拟研究中显示。实际数据结果证实了肿瘤和心血管疾病在确定预期寿命方面在其它研究中出现的重要作用,并揭示了其他一些尚未观察到的贡献。