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：多元函数数据中截面成分数据在统计建模文献中日益受到关注，其中一个典型例子是从特定死因死亡率推导出的成分随时间变化的轨迹。本研究开发了一种新的函数并发回归模型，其中自变量为函数成分。这使得我们能够研究出生时预期寿命与从四个不同年龄组（即0-4岁、5-39岁、40-64岁和65岁以上）的特定死因死亡率推导出的成分之间的时变关系。我们提出了一种惩罚方法来估计回归系数并选择相关变量。然后基于增广拉格朗日算法推导出高效的计算策略，以求解由此产生的优化问题。模拟研究显示了该模型在预测响应函数和估计未知函数系数方面的良好性能。真实数据结果证实了肿瘤和心血管疾病在决定预期寿命中的重要作用——这与其他研究结果一致——并揭示了若干尚未被观察到的其他贡献。