Finite Sample Confidence Regions for Parameters in Prediction Error Identification using Output Error Models

摘要

The purpose of this paper is to evaluate the reliability in finite samples of different methods for constructing probabilistic parameter confidence regions in prediction error identification using Output Error (OE) models. The paper presents alternatives to the "classical method" of constructing asymptotically valid confidence regions, which is based on the asymptotic statistical properties of the parameter estimator. It is shown that if alternative test statistics are used, more reliable confidence regions for finite samples can be obtained. Particularly, it is demonstrated that the use of a test statistic based on the Fisher score allows the construction of exact confidence regions for finite samples.