Worst-case large deviations upper bounds for i.i.d. sequences under ambiguity

Abstract

An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min–max (or max–min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.