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Multivariate functional data that are cross-sectionally compositional dataare attracting increasing interest in the statistical modeling literature, amajor example being trajectories over time of compositions derived fromcause-specific mortality rates. In this work, we develop a novel functionalconcurrent regression model in which independent variables are functionalcompositions. This allows us to investigate the relationship over time betweenlife expectancy at birth and compositions derived from cause-specific mortalityrates of four distinct age classes, namely 0--4, 5--39, 40--64 and 65+ in 25countries. A penalized approach is developed to estimate the regressioncoefficients and select the relevant variables. Then an efficient computationalstrategy based on an augmented Lagrangian algorithm is derived to solve theresulting optimization problem. The good performances of the model inpredicting the response function and estimating the unknown functionalcoefficients are shown in a simulation study. The results on real data confirmthe important role of neoplasms and cardiovascular diseases in determining lifeexpectancy emerged in other studies and reveal several other contributions notyet observed.

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