  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+ 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.
