ABSTRACT

We consider the problem of adaptive estimation in a Gaussian white noise model. An adaptation method is proposed, which is in some sense a combination of two classical approaches: Wiener filter and empirical Bayes approach (both developed long before minimax). This method may be seen as is an alternative to Lepski's method: one can in principle try to apply it (and study its performance) in other statistical models. We discuss an interesting phenomenon of undersmoothing and oversmoothing, which occurs in our estimation problem because of embedded model structure.

This talk is based on joint work with B. Levit.