| 1. |
- Caines, Peter E., et al.
(author)
-
Prediction Error Estimators : Asymptotic Normality and Accuracy
- 1976
-
In: Proceedings of the 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes. ; , s. 652-658
-
Conference paper (peer-reviewed)abstract
- In this paper the asymptotic normality of a large class of prediction error estimators is established. (Prediction error identification methods were introduced in [1] and further developed in [2] and [3].) 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 [5]; 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.
|
|
| 2. |
- Ljung, Lennart, 1946-, et al.
(author)
-
Asymptotic Normality of Prediction Error Estimators for Approximate System Models
- 1978
-
In: Proceedings of the 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes. - Linköping : Linköping University. ; , s. 927-932
-
Reports (other academic/artistic)abstract
- A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and that stationarity is not required.
|
|
| 3. |
- Ljung, Lennart, 1946-, et al.
(author)
-
Asymptotic Normality of Prediction Error Estimators for Approximate System Models
- 1980
-
In: Stochastics. - : Taylor & Francis. - 1744-2508 .- 1744-2516 .- 0090-9491. ; 3:1-4, s. 29-46
-
Journal article (peer-reviewed)abstract
- A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not required
|
|
| 4. |
- Åström, Karl J., et al.
(author)
-
Facing the Challenge of Computer Science in the Industrial Applications of Control
- 1992
-
Reports (other academic/artistic)abstract
- Control, signal processing, and more generally "systems" industries ignore the boundaries we have in the academic world between control, signal processing, and computer sciences. Industries think of "hardware" (electronics or computers) and "software", making little distinction between algorithms development and implementation of them. Acting as a chariman of the IFAC Technical Committee on Theory for the triennium 1990-1993, Albert Benveniste proposed in the fall of 1989 this project to investigate some fundamental questions raised by the above mentioned facts. Since CDC'90 this has been approved as a joint IEEE/CSS-IFAC project managed by the above listed group of people. A detailed progress report of the project has been written in March 20, 1991, followed by a brief update in October 19, 1991. This is summary of the conclusions of the report. Additional detailed information on the project is found in the bibliography.
|
|
