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

TL;DR

This paper introduces a linear regression model for histogram-valued symbolic data using Wasserstein distance, enabling effective prediction of distributional variables with a novel error metric.

Contribution

It develops a least squares estimation approach for symbolic histogram data utilizing Wasserstein distance, extending traditional regression to distributional variables.

Findings

The model accurately predicts histogram responses.

Wasserstein distance effectively measures distributional errors.

Application on real data demonstrates practical utility.

Abstract

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