Summary
We continue our investigation into robust finite experiments and decision problems which we started in part I. We give a short derivation of the Huber-Strassen theorem, and also a proof of a new result on the existence of simultaneously least favorable experiments for contaminated classification problems. The main effort goes into the development of tools which allow us to apply the general results of part I. The principal device needed for our derivations is a reparametrization of decision spaces and a corresponding lift of loss functions which we call “standard loss functions” (in analogy to “standard experiments”). Non robust decision theory which deals with linear functionals (expectations) does not need this device, but robust theory based on sublinear functionals (upper expectations) does.
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Buja, A. Simultaneously least favorable experiments. Z. Wahrscheinlichkeitstheorie verw Gebiete 69, 387–420 (1985). https://doi.org/10.1007/BF00532741
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DOI: https://doi.org/10.1007/BF00532741