  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.
