Minimax approach to some constraint statistical decision models (Q2891123)

The paper focuses mainly on the possibility of interpreting and solving some constrained statistical decision models as specific cases of an infinite dimensional programming problem. The particularity of this problem is the lack of any topological or vector structure on the parameter set. A variety of testing statistical hypotheses models can be obtained for appropriate choices of parameter sets: the most stringent are the Wald test, minimax tests, weighted Krafft's tests, constrained classification, symmetrical multiple tests, constrained classification in non-mutually exclusive and non-exhaustive classes, etc. The author focuses mainly on the existence of optimal solutions of the considered program and on some necessary conditions for an \(n\)-dimensional decision function for being optimal solution. Some sufficient conditions of optimality are derived too. Detailed proofs are shown. Some examples are given.