Applying constrained linear regression models to predict interval-valued data

Billard and Diday [2] were the first to present a regression method for interval-value data. De Carvalho et al [5] presented a new approach that incorporated the information contained in the ranges of the intervals and that presented a better performance when compared with the Billard and Diday method. However, both methods do not guarantee that the predicted values of the lower bounds ((y) over cap (Ui)) will be lower than the predicted values of the upper bounds (qui). This paper presents two approaches based on regression models with inequality constraints that guarantee the mathematical coherence between the predicted values (y) over cap (Li) and (y) over cap (Ui). The performance of these approaches, in relation with the methods proposed by Billard and Diday [2] and De Carvalho et al [5], will be evaluated in framework of Monte Carlo experiments.