Abstract
This paper deals with the problem of estimating the mean of an infinite-dimensional Gaussian vector by the principle of minimizing unbiased risk estimation (URE). The aim is to obtain an adaptive estimator to mimic the oracle with the smallest squared L2 loss/risk in a given class of linear estimators Λ. It is noticed that there is an essential balance between enlarging Λ for more efficient oracle risk and contracting Λ for the adaptivity to the oracle. This paper proves that this balance can be well achieved by minimizing URE in a list of intermediate classes between the projection and monotone classes. The resulting estimators are adaptive on the nonparametric space and have more efficient risks than the projection estimators under certain conditions.
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