The Stein hull

Details The Stein hull The Stein hull

2008-07-14

arxiv.org/abs/0807.2100v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

We are interested in the statistical linear inverse problem $Y=Af+\epsilon\xi$, where $A$ denotes a compact operator and $\epsilon\xi$ a stochastic noise. In a first time, we investigate the link between some threshold estimators and the risk hull point of view introduced in (5). The penalized blockwise Stein's rule plays a central role in this study. In particular, this estimator may be considered as a risk hull minimization method, provided the penalty is well-chosen. Using this perspective, we study the properties of the threshold and propose an admissible range for the penalty leading to accurate results. We eventually propose a penalty close to the lower bound of this range. The risk hull point of view provides interesting tools for the construction of adaptive estimators. It sheds light on the processes governing the behavior of linear estimators. The variability of the problem may be indeed quite large and should be carefully controlled.

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