Application-Oriented Estimator Selection

Designing the optimal experiment for the recovery of an unknown system with respect to the end performance metric of interest is a recently established practice in the system identification literature. This practice leads to superior end performance to designing the experiment with respect to some generic metric quantifying the distance of the estimated model from the true one. This is usually done by choosing and fixing the estimation method to either a standard maximum likelihood (ML) or a Bayesian estimator. In this paper, we pose the intuitive question: Can we design better estimators than the usual ones with respect to an end performance metric of interest? Based on a simple linear regression example we affirmatively answer this question.