Finite sample properties of system identification of ARX models under mixing conditions

Automatica

Volumn 36, Issue 9, 2000, Pages 1291-1299

  Weyer, Erik ^a,b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; INTELLIGENT CONTROL; LEARNING SYSTEMS; MATHEMATICAL MODELS; STABILITY CRITERIA; SYSTEM STABILITY;

LEARNING THEORY; PREDICTION ERROR METHODS;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0034268735     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(00)00039-X     Document Type: Article

References (21)

1. Campi, M. C., & Kumar, P. R. (1998). Learning dynamical systems in a stationary environment. Systems and Control Letters, 34, 125-132.
2. Devroye, L., Györfi, L., & Lugosi, G. (1996). A probabilistic theory of pattern recognition. Berlin: Springer.
3. Doukhan, P. (1994). Mixing-properties and examples. Lecture Notes in Statistics, vol. 85.. Berlin: Springer.
4. Haussler, D. (1992). Decision theoretic generalizations of the PAC model for neural net and other learning applications. Information and Computation, 100, 78-150.
5. Haussler, D. (1995). Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension. Journal of Combinatorial Theory, Series A, 69, 217-232.
6. Hole, A. (1996). Vapnik-Chervonenkis generalization bounds for real valued neural networks. Neural Computation, 8(6), 1277-1299.
7. Huber, P. J. (1981). Robust statistics.. New York: Wiley.
8. Ljung, L. (1987). System identification - theory for the user. Englewood Cliffs, NJ: Prentice-Hall.
9. Meir, R. (1997). Performance bounds of nonlinear time series prediction. Proceedings of the tenth annual conference on computational learning theory (pp. 122-129). New York: ACM Press.
10. Modha, D. S., & Masry, E. (1996). Minimum complexity regression estimation with weakly dependent observations. IEEE Transactions on Information Theory, 42, 2133-2145.
11. Modha, D. S., & Masry, E. (1998). Memory-universal prediction of stationary random processes. IEEE Transactions on Information Theory, 44, 117-133.
12. Mokkadem, A. (1988). Mixing properties of ARMA processes. Stochastic Processes and their Applications, 29, 309-315.
13. Pollard, D. (1984). Convergence of stochastic processes. Berlin: Springer.
14. Söderström, T., & Stoica, P. (1988). System identification. Englewood Cliffs, NJ: Prentice-Hall.
15. Vapnik, V. (1982). Estimation of dependences based on empirical data. Berlin: Springer.
16. Vapnik, V. (1995). The nature of statistical learning theory. Berlin: Springer.
17. Vidyasagar, M. (1997). A theory of learning and generalization. Berlin: Springer.
18. Weyer, E. (1998). Finite sample complexity of system identification with bounded criterion functions. Proceedings of MTNS '98, Padua, Italy, July (pp. 907-910).
19. Weyer, E., Williamson, R. C., & Mareels, I. M. Y. (1996). Sample complexity of least squares identification of FIR models. Proceedings of the 13th world congress of IFAC, vol. J, San Francisco, CA, July (pp. 239-244).
20. Weyer, E., Williamson, R. C., & Mareels, I. M. Y. (1999). Finite sample properties of linear model identification. IEEE Transactions on Automatic Control, 44(1), 1370-1383.
21. Yu, B. (1994). Rates of convergence for empirical processes of stationary mixing sequences. Annals of Probability, 22(1), 94-116.