A1218
Title: Kernel densities as symbolic data for interval-valued composite indicators
Authors: Carlo Drago - University Niccolo Cusano, Rome (Italy) [presenting]
Abstract: Composite indicators summarize multidimensional phenomena but involve subjective choices, particularly in weighting schemes. This framework addresses such uncertainty by treating composite indicators as interval-valued symbolic data. For each statistical unit, a Monte Carlo simulation generates B replications of the composite indicator by sampling the weight vector from a Dirichlet(1,1,1) distribution, which is uniform over the unit simplex. The resulting minimum and maximum define an interval whose midpoint provides a robust central value, while the range quantifies sensitivity to the weighting scheme. Additional interval characteristics, including the bounds and interval length, offer complementary diagnostic information on unit-level uncertainty. Kernel density estimation is then applied to the interval midpoints, producing distribution-valued symbolic descriptions for each group of units. The estimated densities enable nonparametric group comparisons through ridgeline-type visualizations and distributional rankings, capturing heterogeneity patterns that pointwise rankings would obscure. Unlike existing robustness analyses that remain at the unit level, this approach elevates the analysis to the distributional level, connecting composite indicator methodology with symbolic data analysis. The framework is illustrated through a simulation involving world countries and poverty-related indicators, with continental-level density comparisons, and is implemented in R.
