Robust Data-Driven Decisions Under Model Uncertainty

This paper studies how to use sample data to improve decisions robustly when the datagenerating process (DGP) is only known to belong to a set of independent but possibly nonidentical distributions. It proposes two achievable notions of how decisions based on inference from data can improve upon those without using the data no matter which possible DGP governs the uncertainty. When decisions are made according to the maxmin expected-utility criterion, either of these notions is guaranteed if and only if the updated set of DGPs accommodates (contains) the true DGP. In the current setting, common inference methods (e.g., maximum likelihood and Bayesian updating) are shown to often fail this property. This paper proposes two novel and tractable updating rules that accommodate the true DGP either asymptotically almost surely or in finite sample with a pre-specified probability. Finally, it explores implications for applications such as asset pricing under ambiguity.