  We discuss the approach to estimate aggregation and adaptive estimation based
upon (nearly optimal) testing of convex hypotheses. We show that in the
situation where the observations stem from {\em simple observation schemes} and
where set of unknown signals is a finite union of convex and compact sets, the
proposed approach leads to aggregation and adaptation routines with nearly
optimal performance. As an illustration, we consider application of the
proposed estimates to the problem of recovery of unknown signal known to belong
to a union of ellitopes in Gaussian observation scheme. The proposed approach
can be implemented efficiently when the number of sets in the union is "not
very large." We conclude the paper with a small simulation study illustrating
practical performance of the proposed procedures in the problem of signal
estimation in the single-index model.
