Title: Non-asymptotic Bayesian Minimax Adaptation in Gaussian Infinite Sequence Models
Abstract: This paper introduces improved Bayes estimators in a Gaussian infinite sequence model, focusing on the invariance of minimax risk. The parameter is assumed to be in a Sobolev ellipsoid with smoothness $\alpha_0$ and volume $B$ and the noise variance is assumed to be $\varepsilon^2$. In this problem, the minimax risk over a Sobolev ellipsoid is invariant when the value of $B/\varepsilon^2$ is unchanged. However, several existing estimators that are asymptotically minimax as $\varepsilon \to 0$ lack this invariance. To recover the invariance, our attention is focused on non-asymptotic minimax adaptation. We construct a non-asymptotically minimax adaptive Bayes estimator. We also present several numerical experiments demonstrating the performance of the proposed Bayes estimator.
Publication Year: 2016
Publication Date: 2016-09-04
Language: en
Type: preprint
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