A bootstrap method for structure detection of NARMAX models

International Journal of Control

Volumn 77, Issue 2, 2004, Pages 132-143

  Kukreja, Sunil L ^a,b   Galiana, Henrietta L ^a   Kearney, Robert E ^a  

^a MCGILL UNIVERSITY   (Canada)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; MONTE CARLO METHODS; NONLINEAR CONTROL SYSTEMS; PROBABILITY DISTRIBUTIONS; STATISTICS;

BOOTSTRAP STRUCTURE DETECTION ALGORITHM; HIGHLY OVER-PARAMETERIZED MODEL;

PARAMETER ESTIMATION;

EID: 1342326270     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207170310001646264     Document Type: Article

References (31)

1. Bickel, P. J., and Freedman, D. A., 1981, Some asymptotic theory for the bootstrap. The Annals of Statistics, 9, 1196-1217.
2. Bickel, P. J., and Freedman, D. A., 1982, Bootstrapping regression models with many parameters. Technical Report 7. Department of Statistics, University of California (Berkeley), Berkeley, California.
3. Billings, S. A., and Voon, W. S. F., 1984, Least squares parameter estimation algorithms for non-linear systems. International Journal of System Science, 15, 601-615.
4. Box, G. E. P., and Jenkins, G. M., 1970, Time Series Analysis: Forecasting and Control, 1st edn (San Francisco: Holden-Day).
5. Chen, S., Billings, S. A., and Luo, W., 1989, Orthogonal least squares methods and their applications to nonlinear system identification. International Journal of Control, 50, 1873-1896.
6. Copas, J. B., 1983, Regression, prediction and shrinkage. Journal of the Royal Statistical Society B, 45, 311-354.
7. Draper, N. R., and Smith, H., 1981, Applied Regression Analysis, 2nd edn (New York: Wiley).
8. Efron, B., 1979, Computer and the theory of statistics: Thinking the unthinkable. SIAM Review, 21, 460-480.
9. Efron, B., and Tibshirani, R. J., 1993, An Introduction to the Bootstrap, 1st edn (New York: Chapman and Hall).
10. Efroymson, M. A., 1960, Multiple regression and correlation. In Mathematical Methods for Digital Computers, 1st edn (New York: Wiley).
11. Freedman, D. A., 1981, Bootstraping regression models. The Annals of Statistics, 9, 1218-1228.
12. Goodwin, G. C., and Payne, R. L., 1977, Dynamic System Identification: Experiment Design and Data Analysis. Vol. 136 of Mathematics in Science and Engineering (New York: Academic).
13. Haber, R., and Unbehauen, H., 1990, Structure identification of nonlinear dynamic systems-a survey on input/output approaches. Automatica 26, 651-677.
14. Hsia, T. C., 1977, System Identification: Least-Squares Methods (Lexington, MA: Lexington Books, D. C. Heath and Company).
15. Hurvich, C. M., and Tsai, C. L., 1990, The impact of model selection on inference in linear regression. The American Statistician, 44, 214-217.
16. Korenberg, M. J., 1985, Orthogonal identification of nonlinear difference equation models. Proceedings of the Midwest Symposium on Circuit Theory, 1, 90-95.
17. Korenberg, M. J., 1989, A robust orthogonal algorithm for system identification and time series analysis. Biological Cybernetics, 60, 267-276.
18. Korenberg, M. J., Billings, S. A, Liu, Y. P., and McIlroy, P. J., 1988, Orthogonal parameter estimation algorithm for non-linear stochastic systems. International Journal of Control, 48, 193-210.
19. Kukreja, S. L., Galiana, H. L., and Kearney, R. E., 1999, Structure detection of NARMAX models using bootstrap methods. In Proceedings of the 38th IEEE Conference on Decision and Control, Vol. 38, Phoenix, AZ, USA, pp. 1071-1076.
20. Kukreja, S. L., Kearney, R. E., and Galiana, H. L., 1998, Structure detection of nonlinear dynamic systems using bootstrap methods. In Proceedings of the IEEE EMBS, Vol. 20, Hong Kong, China. pp. 3020-3023.
21. Leontaritis, I. J., and Billings, S. A., 1985, Input-output parametric models for non-linear systems part I: deterministic non-linear systems. International Journal of Control, 41, 303-328.
22. Ljung, L., 1999, System Identification: Theory for the User, 2nd edn (Englewood Cliffs, NJ: Prentice Hall).
23. Mantel, M., 1970, Why stepdown procedures in variable selection. Technometrics, 12, 621-625.
24. Miller, A. J., 1996, The convergence of Efroymson's stepwise regression algorithm. The American Statistician, 50, 180-181.
25. Panuska, V., 1968, A stochastic approximation method for identification of linear systems using adaptive filtering. In Proceedings 9th Joint Automatic Control Conference, IEEE, Ann Arbor, MI, USA, pp. 1014-1021.
26. Panuska, V., 1969, An adaptive recursive least squares identification algorithm. In Proceedings 8th IEEE Symposium on Adaptive Processes, University Park, PA, USA, Paper 6e.
27. Seber, G. A. F., 1977, Linear Regression Analysis, 1st edn (New York: Wiley).
28. Sjöberg, J., Zhang, Q., Ljung, L., Delyon, B., Benveniste, A., Glorennec, P. Y., Hjalmarsson, H., and Juditsky, A., 1995, Nonlinear black-box modeling in system identification: a unified overview. Automatica, 31, 1691-1724.
29. Young, P. C., 1968, The use of linear regression and relaxed procedures for the identification of dynamic processes. In: Proceedings of the 7th IEEE Symposium on Adaptive Processes, Los Angeles, CA, USA, pp. 501-505.
30. Young, P. C., 2000, Stochastic, dynamic modelling and signal processing: Time variable and state dependent parameter estimation. In Nonstationary and nonlinear signal processing (Cambridge: Cambridge University Press), pp. 74-114.
31. Young, P. C., McKenna P., and Bruun, J., 2001, Identification of nonlinear stochastic systems by state dependent parameter estimation. International Journal of Control, 74, 1837-1957.