The Stein hull

Abstract

International audienceWe are interested in the statistical linear inverse problem $Y=Af+\epsilon \xi$, where $A$ denotes a compact operator and $\xi$ a stochastic noise. In this setting, the risk hull point of view provides interesting tools for the construction of adaptive estimators. It sheds light on the processes governing the behaviour of linear estimators. In this paper, we investigate the link between some threshold estimators and this risk hull point of view. The penalized blockwise Stein 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 accu- rate results. We eventually propose a penalty close to the lower bound of this range