  We address the statistical issue of determining the maximal spaces (maxisets)
where model selection procedures attain a given rate of convergence. By
considering first general dictionaries, then orthonormal bases, we characterize
these maxisets in terms of approximation spaces. These results are illustrated
by classical choices of wavelet model collections. For each of them, the
maxisets are described in terms of functional spaces. We take a special care of
the issue of calculability and measure the induced loss of performance in terms
of maxisets.
