Paper: Maximum-power validation of models without higher-order fitting

• Authors: Torsten Bohlin
• Venue: Automatica (Journal of IFAC)
• Year: 1978

A new solution is presented to the problem of validating optimally a given dynamic model against given long-sample observations. If the model can be parametrized and cast into a general innovations structure, i.e. if expressions for the one-step predictor and the prediction error covariances are available, a test can be constructed that has asymptotic maximum discriminating power, for the least favourable case that the difference to be detected between model and observed system is small. A class of alternative models must be specified, but, unlike in other optimal tests, it is not required also to fit a best model within this class. Since the alternative class may include models more complicated than that to be validated, the test can be used for recursive determination of structure and order. For linear transfer-function or polynomial-operator models the asymptotic maximum-power test does not require much more computing, and sometimes less, than the conventional tests of auto- and cross-correlation. Generally, the latter tests are less efficient, even for linear models, if these is some a priori knowledge about the structure. A simple example demonstrates that there are realistic cases where the asymptotic maximum-power test may be considerably better.