On Asymptotic Analysis of the Two-Stage Approach: Towards Data-Driven Parameter Estimation

Abstract: In this paper, we analyze the asymptotic properties of the Two-Stage (TS) estimator -- a simulation-based parameter estimation method that constructs estimators offline from synthetic data. While TS offers significant computational advantages compared to standard approaches to estimation, its statistical properties have not been previously analyzed in the literature. Under simple assumptions, we establish that the TS estimator is strongly consistent and asymptotically normal, providing the first theoretical guarantees for this class of estimators.