A Clusterwise regression method for Distributional-valued Data

In this paper we propose a cluster-wise regression strategy for aggregated data represented by distributions. The basic idea is that the set of observed data are related by local causal relationships for different clusters. Some cluster-wise regres- sion methods are based on K-means clustering algorithms, where the representa- tives of clusters are expressed by linear models and the assignment of an element to a cluster is performed according to the minimum distance to the model, in the sense of ordinary least squares (OLS). The proposed method extends this strategy to data expressed by empirical distributions or histograms. The present work refers to one of the regression models proposed in the analysis of the dependence of his- togram type variables and to the k-means algorithm developed for such data. The metric used is the L2 Wasserstein distance. An application on real distributional data corroborate the method.