Prediction Error Estimators: Asymptotic Normality and Accuracy
1976 (English)In: Proceedings of the 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, 1976, 652-658 p.Conference paper (Refereed)
In this paper the asymptotic normality of a large class of prediction error estimators is established. (Prediction error identification methods were introduced in  and further developed in  and .) The observed processes in this paper are assumed to be stationary and ergodic and the parameterized process models are taken to be non-linear regression models. In the gaussian case the results presented in this paper constitute substantial generalizations of previous results concerning the asymptotic normality of maximum likelihood estimators for (i) processes of independent random variables [9,4] and (ii) Markov processes ; these results also generalize previous results on the asymptotic normality of least squares estimators for autoregressive moving average processes [6,7]. The asymptotic normality theorem gives formulae for the covariances of the asymptotic distributions of the parameter estimation errors arising from the specified class of prediction error identification methods. Employing these formulae it is demonstrated that the prediction error method using the determinant of the residual error covariance matrix as loss function is asymptotically efficient with respect to the specified class of prediction error estimators regardless of the distribution of the observed processes.
Place, publisher, year, edition, pages
1976. 652-658 p.
Asymptotic, Prediction error estimator, Markov processes, Maximum likelihood, Covariance matrix
IdentifiersURN: urn:nbn:se:liu:diva-100844DOI: 10.1109/CDC.1976.267809OAI: oai:DiVA.org:liu-100844DiVA: diva2:664017
1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, Clearwater, FL, USA, December, 1976