Aggregating estimates by convex optimization

We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. show that in situation where observations stem from simple observation schemes (Juditsky Nemirovski, 2020) set unknown signals is a finite union compact sets, proposed leads adaptation routines with nearly optimal performance. As an illustration, we consider application estimates problem recovery signal known belong ellitopes 2018 Gaussian scheme. The can be implemented efficiently when number sets “not very large.” conclude paper small simulation study illustrating practical performance procedures single-index model.