Recently Y. Meyer derived a characterization of the minimizer of
the Rudin-Osher-Fatemi functional in a functional analytical framework.
In statistics the discrete version of this functional is used
to analyze one dimensional data and belongs to the class of nonparametric regression models.
In this work we generalize the functional analytical results of Meyer and apply them
to a class of regression models, such as quantile, robust, logistic regression,
for the analysis of multidimensional data. The characterization of Y. Meyer
and our generalization is based on G-norm properties of the data and the minimizer.
A geometric point of view of regression minimization is provided.