Guaranteed non-asymptotic confidence regions in system identification

Automatica

Volumn 41, Issue 10, 2005, Pages 1751-1764

  Campi, Marco Claudio ^a   Weyer, Erik ^b  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Confidence sets; Finite sample results; General linear models; System identification; Uncertainty evaluation

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; MATHEMATICAL MODELS; PROBABILITY; PROBLEM SOLVING; UNCERTAIN SYSTEMS;

CONFIDENCE SETS; FINITE SAMPLE RESULTS; GENERAL LINEAR MODELS; UNCERTAINTY EVALUATION;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 23744480441     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.05.005     Document Type: Article

References (25)

1. E.W. Bai, K.M. Nagpal, and R. Tempo Bounded-error parameter estimation: Noise models and recursive algorithms Automatica 32 1996 985 999
2. E.W. Bai, R. Tempo, and H. Cho Membership set estimators: Size, optimal inputs, complexity and relations with least squares IEEE Transactions on Circuits and Systems 42 5 1995 266 277
3. S. Bittanti, and M. Lovera Bootstrap-based estimates of uncertainty in subspace identification methods Automatica 36 2000 1605 1615
4. Campi, M. C., & Garatti, S. (2003). Correlation approach for ARMAX model identification: A counterexample on the uniqueness of the asymptotic solution. Internal Report of the University of Brescia.
5. M.C. Campi, S.K. Ooi, and E. Weyer Non-asymptotic quality assessment of generalised FIR models with periodic inputs Automatica 40 12 2004 2029 2041
6. M.C. Campi, and E. Weyer Finite sample properties of system identification methods IEEE Transactions on Automatic Control AC-47 2002 1329 1334
7. Campi, M. C., & Weyer, E. (2004). Non-asymptotic confidence sets for the parameters of ARMAX models. IFAC workshop on adaptation and learning in control and signal processing (ALCOSP 2004) (pp. 841-846). Yokohama, Japan.
8. Campi, M. C., & Weyer, E. (2005). Guaranteed non-asymptotic confidence regions in system identification. Internal Report, University of Brescia. Available on request from the authors and available at http://bsing.ing.unibs.it/~campi/ and http://www.ee.unimelb.edu.au/staff/ewey/.
9. Garatti, S., Campi, M. C., & Bittanti, S. (2003). Model quality assessment for instrumental variable methods: Use of the asymptotic theory in practice. In Proceeding of the 42nd conference on decision and control, Maui, USA.
10. S. Garatti, M.C. Campi, and S. Bittanti Assessing the quality of identified models through the asymptotic theory - When is the result reliable? Automatica 40 8 2004 1319 1332
11. A. Garulli, L. Giarre', and G. Zappa Identification of approximated Hammerstein models in a worst-case setting IEEE Transactions on Automatic Control 47 2002 2046 2050
12. A. Garulli, A. Vicino, and G. Zappa Conditional central algorithms for worst-case set membership identification and filtering IEEE Transactions on Automatic Control 45 1 2000 14 23
13. L. Giarre', B.Z. Kacewicz, and M. Milanese Model quality evaluation in set membership identification Automatica 33 6 1997 1133 1139
14. L. Giarre', M. Milanese, and M. Taragna H ∞ identification and model quality evaluation IEEE Transactions on Automatic Control 4 1997 88 199
15. L. Gordon Completely separating groups in subsampling Annals of Statistics 2 1974 572 578
16. J.A. Hartigan Using subsample values as typical values Journal of American Statistical Association 64 1969 1303 1317
17. J.A. Hartigan Exact confidence intervals in regression problems with independent symmetric errors Annals of Mathematical Statistics 41 1970 1992 1998
18. L. Ljung System identification - theory for the user (2nd ed.) 1999 Prentice-Hall Englewood-Cliffs, NJ
19. Ljung, L. (1999b). Model validation and model error models. In Wittenmark B., Rantzer A. (Eds.). The Åström symposium on control (pp. 15-42). Studentlitteratur, Lund, Sweden.
20. L. Ljung Estimating linear time-invariant models of nonlinear time-varying systems European Journal of Control 7 2001 203 219
21. M. Milanese, and A. Vicino Optimal estimation theory for dynamic systems with set membership uncertainty: An overview Automatica 27 6 1991 997 1009
22. T. Söderström, and P. Stoica System identification 1988 Prentice-Hall Englewood-Cliffs, NJ
23. F. Tjärnström, and L. Ljung Using the bootstrap to estimate the variance in the case of undermodelling IEEE Transactions on Automatic Control 47 2 2002 395 398
24. A. Vicino, and G. Zappa Sequential approximation of feasible parameter sets for identification with set membership uncertainty IEEE Transactions on Automatic Control 41 1996 774 785
25. E. Weyer, and M.C. Campi Non-asymptotic confidence ellipsoids for the least squares estimate Automatica 38 9 2002 1539 1547