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The Stein hull

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  • Clément Marteau

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.

Suggested Citation

  • Clément Marteau, 2010. "The Stein hull," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 685-702.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:685-702
    DOI: 10.1080/10485250903388878
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    1. Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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