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Abstract:
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We apply the Bayes approach to the problem of projection estimation of the signal observed in Gaussian white noise model and we study the rate at which the posterior distribution concentrates around the true signal, as the information in the observations tends to infinity. A benchmark is the rate of the so called oracle projection risk, i.e. the smallest risk of the unknown true signal over all projection estimators. Under appropriate hierarchical prior, we construct a posterior-randomized estimator for the cut-off parameter of the projection estimator and show that the resulting adaptive projection estimator for the signal satisfies an oracle risk inequality. Finally, we establish that the appropriately shifted resulting posterior concentrates around the true signal with the oracle projection convergence rate.
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