Universal confidence sets - sufficient conditions

Universal confidence sets for solutions of optimization problems are sequences of random sets (C_n)_{n \in N} with the property that for each sample size n the set C_n covers the true solution at least with a prescribed probability. Universal confidence sets can be derived making use of uniform concentration-of-measure results for sequences of random functions and knowledge about the limit problem, e.g. a growth condition. We present sufficient conditions for the convergence assumptions and show how estimates for the growth function can be included.


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