Abstract
Composite indicators are reliable tools that have recently gained popularity because of their effectiveness in solving problems of multidimensional measurement. Along with the notable increase in the number of applications, finding optimal weights for input features during aggregation is a topic that creates many controversies but very few radical solutions. This paper presents a novel statistical method designed to assist developers in attaining a plausible weighting scheme for composite indices. The solution obtained is referred to as sensitivity-based weights, where the magnitude of each weight aligns with the proportion of output variance contributed by the corresponding input. Within the context of our theoretical framework, these weights can be identified based on the multivariate distribution of input features. In case the population distribution is unknown, we introduce an optimization procedure for estimating sensitivity-based weights from a finite sample of inputs. Two supporting algorithms are proposed to facilitate the weighting process, including regression-based estimation and coarse estimation. These algorithms are tested in two numerical simulation cases, where the results show that the paramount factor affecting the accuracy and robustness of estimates lies in the sample size, and the coarsening technique exhibits superiority in performance when dealing with inputs from various distributions. Finally, a composite index for identifying fragile municipalities in Italy has been examined and reconstructed to demonstrate the method’s applicability in practice.