  Many methods have been developed to estimate the set of relevant variables in
a sparse linear model Y= XB+e where the dimension p of B can be much higher
than the length n of Y. Here we propose two new methods based on multiple
hypotheses testing, either for ordered or non-ordered variables. Our procedures
are inspired by the testing procedure proposed by Baraud et al (2003). The new
procedures are proved to be powerful under some conditions on the signal and
their properties are non asymptotic. They gave better results in estimating the
set of relevant variables than both the False Discovery Rate (FDR) and the
Lasso, both in the common case (p<n) and in the high-dimensional case (p>n).
