Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance

摘要

In this paper we present a linear regression model for modal symbolic data.The observed variables are histogram variables according to the definitiongiven in the framework of Symbolic Data Analysis and the parameters of themodel are estimated using the classic Least Squares method. An appropriatemetric is introduced in order to measure the error between the observed and thepredicted distributions. In particular, the Wasserstein distance is proposed.Some properties of such metric are exploited to predict the response variableas direct linear combination of other independent histogram variables. Measuresof goodness of fit are discussed. An application on real data corroborates theproposed method.