The Stein hull

Clément Marteau

Journal of Nonparametric Statistics, 2010, vol. 22, issue 6, 685-702

Abstract: We are interested in the statistical linear inverse problem Y=Af+εξ, where A denotes a compact operator and εξ 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 article, we investigate the link between some threshold estimators and this risk hull point of view. The penalised blockwise Stein rule plays a central role in this study. In particular, this estimator may be considered as a risk hull minimisation 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.

Date: 2010
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DOI: 10.1080/10485250903388878

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