Non-asymptotic quality assessment of generalised FIR models with periodic inputs

Abstract

In any real-life identification problem, only a finite number of data points is available. On the other hand, almost all results in stochastic identification pertain to asymptotic properties, that is they tell us what happens when the number of data points tends to infinity. In this paper we consider the problem of assessing the quality of the estimates identified from a finite number of data points. We focus on least squares identification of generalised FIR models and develop a method to produce a bound on the uncertainty in the parameter estimate. The method is data driven and based on tests involving permuted data sets. Moreover, it does not require that the true system is in the model class.