Non-asymptotic quality assessment of generalised FIR models with periodic inputs

Automatica

Volumn 40, Issue 12, 2004, Pages 2029-2041

  Campi, M C ^a   Ooi, Su Ki ^b   Weyer, E ^b  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Confidence sets; Finite samples properties; Half samples; Least squares; Model validation; System identification

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; PARAMETER ESTIMATION; PROBABILITY;

CONFIDENCE SETS; FINITE SAMPLES PROPERTIES; HALF SAMPLES; MODEL VALIDATION;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 5444225695     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2004.06.020     Document Type: Article

References (31)

1. Bittanti, S., Campi, M. C., & Garatti, S. (2002). New result on the asymptotic theory of system identification for the assessment of the quality of estimated models. Proceedings of the 41st IEEE CDC, Las Vegas, Nevada, USA. (pp. 1814-1819).
2. Campi, M. C., & Weyer, E. (2002). Finite sample properties of system identification methods. IEEE Transactions on Automatic Control, 47(8), 1329-1334.
3. Chen, J., & Gu, G. (2000). Control oriented system identification. An H∞ approach. New York: Wiley.
4. Garatti, S., Campi, M. C., & Bittanti, S. (2004). Assessing the quality of identified models through the asymptotic theory - When is the result reliable?. Automatica, 40(8), 1319-1332.
5. 2 identification. Automatica, 33, 1133-1139.
6. Good, P. (2000). Permutation tests: a practical guide to resampling methods for testing hypotheses. 2nd ed., Berlin: Springer.
7. Goodwin, G. C., Gevers, M., & Ninness, B. (1992). Quantifying the errors in estimated transfer functions with application to model order selection. IEEE Transactions on Automatic Control, 37(1), 913-928.
8. Hakvoort, R. G., & Van den Hof, P. M. (1997). Identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors. IEEE Transactions on Automatic Control, 42(11), 1516-1528.
9. Hartigan, J. A. (1969). Using subsample values as typical values. Journal of the American Statistical Association, 64(328), 1303-1317.
10. Koltchinskii, V. (2001). Rademacher penalties and structural risk minimization. IEEE Transactions Information Theory, 47(6), 1902-1914.
11. Koltchinskii, V., & Panchenko, D. (2000). Rademacher processes and bounding the risk of function learning, in: Gine, Mason, & Wellner (Eds.), High dimensional probability II. (pp. 443-459). Basel: Birkhäuser.
12. Lehmann, E. L. (1986). Testing statistical hypotheses. 2nd ed., New York: Wiley, Reprinted (1994) edition by Chapman and Hall.
13. Ljung, L. (1999). System identification theory for the user. 2nd ed., Englewood Cliffs: Prentice-Hall.
14. Ljung, L. (2001). Estimating linear time invariant models of non-linear time-varying systems. European Journal of Contral, 7(2-3), 203-219.
15. Ljung, L., & Guo, L. (1997). The role of model validation for assessing the size of the unmodeled dynamics. IEEE Transactions on Automatic Control, 42(9), 1230-1239.
16. Manolakis, D. G., Ingle, V. K., & Kogon, S. M. (2000). Statistical and adaptive signal processing. New York: McGraw-Hill.
17. McCarthy, P. J. (1969). Pseudo-replication: half samples. Review of The International Statistical Institute, 37, 239-263.
18. Mendelson, S. (2002). Rademacher averages and phase transition in Glivenko-Cantelli classes. IEEE Transactions Information Theory, 48(1), 251-263.
19. Milanese, M., & Taragna, M. (2002). Optimally, approximation and complexity in set membership H∞ identification. IEEE Transactions on Automatic Control, 47(10), 1682-1690.
20. Ooi, S. K., Weyer, E., & Campi, M. C. (2003). Finite sample quality assessment of system identification models of irrigation channels. Proceedings of the IEEE conference on control application, Istanbul, Turkey.
21. Politis, D. N., Romano, J. P., & Wolf, M. (1999). Subsampling. Berlin: Springer.
22. Richmond, S. (1964). Statistical analysis. 2nd ed., New York: The Ronald Press Company.
23. Söderström, T., & Stoica, P. (1988). System identification. Englewood Cliffs: Prentice-Hall.
24. Tjärnström, F., & Ljung, L. (2002). Using the Bootstrap to estimate the variance in the case of undermodeling. IEEE Transactions on Automatic Control, 47(2), 395-398.
25. Van der Vaart, A. W. (1998). Asymptotic statistics. Cambridge: Cambridge University Press.
26. Vidyasagar, M. (1997). A theory of learning and generalization with applications to neural networks and control systems. Berlin: Springer.
27. Wahlberg, B., & Ljung, L. (1992). Hard frequency-domain model error bounds from least-squares like identification techniques. IEEE Transactions on Automatic Control, AC-37, 900-912.
28. Welsh, J. S., & Goodwin, G. C. (2002). Finite sample properties of indirect nonparametric closed-loop identification. IEEE Transactions on Automatic Control, 47(8), 1277-1292.
29. Weyer, E. (2000). Finite sample properties of system identification of ARX models under mixing conditions. Automation, 36, 1291-1299.
30. Weyer, E., & Campi, M. C. (1999). Finite sample properties of system identification methods. Proceedings of the 38th IEEE CDC, Phoenix, Arizona, USA. (pp. 510-515).
31. Weyer, E., & Campi, M. C. (2002). Non-asymptotic confidence ellipsoids for the least squares estimate. Automatica, 38(9), 1539-1547.