  One of the most important problems in system identification and statistics is
how to estimate the unknown parameters of a given model. Optimization methods
and specialized procedures, such as Empirical Minimization (EM) can be used in
case the likelihood function can be computed. For situations where one can only
simulate from a parametric model, but the likelihood is difficult or impossible
to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to
obtain reliable parametric estimates. Unfortunately, there is currently a lack
of theoretical justification for TS. In this paper, we propose a statistical
decision-theoretical derivation of TS, which leads to Bayesian and Minimax
estimators. We also show how to apply the TS approach on models for independent
and identically distributed samples, by computing quantiles of the data as a
first step, and using a linear function as the second stage. The proposed
method is illustrated via numerical simulations.

Methodology;Systems and Control;Systems and Control;Machine Learning