  The use of variable selection methods is particularly appealing in
statistical problems with functional data. The obvious general criterion for
variable selection is to choose the `most representative' or `most relevant'
variables. However, it is also clear that a purely relevance-oriented criterion
could lead to select many redundant variables. The mRMR (minimum Redundance
Maximum Relevance) procedure, proposed by Ding and Peng (2005) and Peng et al.
(2005) is an algorithm to systematically perform variable selection, achieving
a reasonable trade-off between relevance and redundancy. In its original form,
this procedure is based on the use of the so-called mutual information
criterion to assess relevance and redundancy. Keeping the focus on functional
data problems, we propose here a modified version of the mRMR method, obtained
by replacing the mutual information by the new association measure (called
distance correlation) suggested by Sz\'ekely et al. (2007). We have also
performed an extensive simulation study, including 1600 functional experiments
(100 functional models $\times$ 4 sample sizes $\times$ 4 classifiers) and
three real-data examples aimed at comparing the different versions of the mRMR
methodology. The results are quite conclusive in favor of the new proposed
alternative.
