A simulation-based estimation method for bias reduction

Models are often built to evaluate system performance measures or to make quantitative decisions. These models sometimes involve unknown input parameters that need to be estimated statistically using data. In these situations, a statistical method is typically used to estimate these input parameters and the estimates are then plugged into the models to evaluate system output performances. The output performance estimators obtained from this approach usually have large bias when the model is nonlinear and the sample size of the data is finite. A simulation-based estimation method to reduce the bias of performance estimators for models that have a closed-form expression already exists in the literature. In this article, we extend that method to more general situations where the models have no closed-form expression and can only be evaluated through simulation. A stochastic root-finding problem is formulated to obtain the simulation-based estimators and several algorithms are designed. Furthermore, we give a thorough asymptotic analysis of the properties of the simulation-based estimators, including the consistency, the order of the bias, the asymptotic variance, and so on. Our numerical experiments show that the experimental results are consistent with the theoretical analysis.