Estimate aggregation from indirect observations
Résumé
We consider the problem of point aggregation and adaptive estimation from indirect observations. The approach we promote relies upon near-optimal testing of convex hypotheses. We show that in the classical problem of $\ell_2$-aggregation the proposed algorithms are near-optimal in different observation settings (e.g, indirect Gaussian observations, Poisson observation model and sampling from discrete distributions). We also discuss the closely related problem of adaptive estimation. The construction of aggregation procedures reduces to convex optimization problems and can be implemented efficiently.