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

TL;DR

This paper provides the first theoretical analysis of the Two-Stage estimator, demonstrating its strong consistency and asymptotic normality, thus establishing its statistical validity alongside its computational benefits.

Contribution

It offers the first rigorous asymptotic analysis of the Two-Stage estimator, confirming its statistical properties under simple assumptions.

Findings

TS estimator is strongly consistent

TS estimator is asymptotically normal

Provides theoretical guarantees for simulation-based 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.