  We propose a method for variable selection in multiple regression with random
predictors. This method is based on a criterion that permits to reduce the
variable selection problem to a problem of estimating suitable permutation and
dimensionality. Then, estimators for these parameters are proposed and the
resulting method for selecting variables is shown to be consistent. A
simulation study that permits to gain understanding of the performances of the
proposed approach and to compare it with an existing method is given.
