Summary
A concept of worst-case-sufficiency is defined, generalizing Le Cam's approximate sufficiency. Instead of using total variation norm, as did Le Cam (1964), neighborhoods are described by upper expectations. A corresponding version of the theorem of Le Cam-Blackwell-Sherman-Stein is proved in the case of finite parameter space. As a main tool serve standard experiments and their upper limits, here to be called upper standard functionals. A characterization of simultaneously least favorable experiments dominated by a family of upper expectations is proved. It says that least favorable experiments exist if and only if the upper standard functional acts additively on a cone of concave functions.
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Part I is essentially from the author's dissertation submitted in partial fulfilment for the Ph.D. degree in Mathematics at the Swiss Federal Institute of Technology
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Buja, A. Simultaneously least favorable experiments. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 367–384 (1984). https://doi.org/10.1007/BF00533742
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DOI: https://doi.org/10.1007/BF00533742