Ordinary Least Squares for histogram data based on Wasserstein distance

Histogram data is a kind of symbolic representation which allows to describe an individual by an empirical frequency distribution. In this paper we introduce a linear regression model for histogram variables. We present a new Ordinary Least Square approach for the model estimation, using the Wasserstein metric between histograms. After having illustrated the concurrent approaches, we corroborate the proposed estimation method by an application on a real dataset.