Applying Constrained Linear Regression Models to Predict Interval-Valued Data

摘要

Billard and Diday 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_(L i)) will be lower than the predicted values of the upper bounds (y_(U i)). This paper presents two approaches based on regression models with inequality constraints that guarantee the mathematical coherence between the predicted values y_(L i) and y_(U i). The performance of these approaches, in relation with the methods proposed by Billard and Diday and De Carvalho et al [5], will be evaluated in framework of Monte Carlo experiments.