  This paper deals with variable selection in the regression and binary
classification frameworks. It proposes an automatic and exhaustive procedure
which relies on the use of the CART algorithm and on model selection via
penalization. This work, of theoretical nature, aims at determining adequate
penalties, i.e. penalties which allow to get oracle type inequalities
justifying the performance of the proposed procedure. Since the exhaustive
procedure can not be executed when the number of variables is too big, a more
practical procedure is also proposed and still theoretically validated. A
simulation study completes the theoretical results.
