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math.ST2022
Statistical minimax theorems via nonstandard analysis
Haosui Duanmu, Daniel M. Roy, David Schrittesser
For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a gener…
math.ST2021
Admissibility is Bayes optimality with infinitesimals
Haosui Duanmu, Daniel M. Roy, David Schrittesser
We give an exact characterization of admissibility in statistical decision problems in terms of Bayes optimality in a so-called nonstandard extension of the original decision probl…