  The selection of grouped variables using the random forest algorithm is
considered. First a new importance measure adapted for groups of variables is
proposed. Theoretical insights into this criterion are given for additive
regression models. Second, an original method for selecting functional
variables based on the grouped variable importance measure is developed. Using
a wavelet basis, it is proposed to regroup all of the wavelet coefficients for
a given functional variable and use a wrapper selection algorithm with these
groups. Various other groupings which take advantage of the frequency and time
localization of the wavelet basis are proposed. An extensive simulation study
is performed to illustrate the use of the grouped importance measure in this
context. The method is applied to a real life problem coming from aviation
safety.
