Functional concurrent regression with compositional covariates and its application to the time-varying effect of causes of death on human longevity

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 causespecific 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, zero to four, five to 39, 40-64 and 65+ in 25 countries. 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.