On the Generalization Performance of a Regression Model with Imprecise Elements

A linear regression model for imprecise random variables is considered. The imprecision of a random element has been formalized by means of the LR fuzzy random variable, characterized by a center, a left and a right spread. In order to avoid the non-negativity conditions the spreads are transformed by means of two invertible functions. To analyze the generalization performance of that model an appropriate prediction error is introduced, a bootstrap procedure is analyzed and it is discussed how to estimate it. Furthermore, since the choice of response transformations could affect the inferential procedures a computational proposal is introduced for choosing from a family of parametric link functions, the Box-Cox family, the transformation parameters that minimize the prediction error of the model.