Fitting a Least Absolute Deviation Regression Model on Interval-Valued Data

Abstract

This paper introduces a least absolute deviation (LAD) regression model suitable for manage interval-valued data. Each example of the data set is described by a feature vector where each feature value is an interval. In the approach, it is fitted two LAD regressions, respectively, on the mid-point and range of the interval values assumed by the variables. The prediction of the lower and upper bound of the interval value of the dependent variable is accomplished from its mid-point and range which are estimated from the fitted LAD regression models applied to the mid-point and range of each interval values of the independent variables. The evaluation of the proposed prediction method is based on the estimation of the average behaviour of root mean squared error and of the correlation coefficient in the framework of a Monte Carlo experience in comparison with the method proposed in [5].