Dipartimento di Scienze Statistiche

Confidence intervals for the parameters of a linear regression model with a fuzzy response variable and a set of real and/or fuzzy explanatory variables are investigated. The family of LR fuzzy random variables is considered and an appropriate metric is suggested for coping with this type of variables. A class of linear regression models is then proposed for the center and for suitable transforms of the spreads in order to satisfy the non-negativity conditions for the latter ones. In order to estimate the regression parameters confidence intervals are introduced and discussed. Since there are no parametric models for the imprecise variables, a bootstrap approach has been used. The empirical behavior of the procedure is analyzed by means of simulated data and a real-case study.