Inverse regression for the wiener class of systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue PART 1, 2012, Pages 476-481

  Lyzell, Christian ^a   Enqvist, Martin ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Dimension reduction; Inverse regression; System identification

Indexed keywords

DIMENSIONALITY REDUCTION; DYNAMICAL SYSTEMS; IDENTIFICATION (CONTROL SYSTEMS); NONLINEAR DYNAMICAL SYSTEMS; REGRESSION ANALYSIS; RELIGIOUS BUILDINGS;

DIMENSION REDUCTION; HIGH-DIMENSIONAL; IDENTIFICATION OF SYSTEMS; INVERSE REGRESSION; LINEAR SUBSYSTEMS; MULTIPLE INPUT SINGLE OUTPUTS; NONLINEAR REGRESSION PROBLEMS; SLICED INVERSE REGRESSIONS;

INVERSE PROBLEMS;

EID: 84867037029     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20120711-3-BE-2027.00286     Document Type: Conference Paper

References (25)

1. S. Boyd and L. O. Chua. Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Transactions on Curcuits and Systems, 32 (11), 1985.
2. E. Bura. Using linear smoothers to assess the structural dimension of regressions. Statistica Sinica, 13, 2003.
3. E. Bura and R. D. Cook. Estimating the structural dimension of regressions via parametric inverse regression. Journal of the Royal Statistical Society: Series B, 63(2): 393-410, 2001.
4. E. Bura and J. Yang. Dimension estimation in sufficient dimension reduction: A unifying approach. Journal of Multivariate Analysis, 102(1):130-142, 2011.
5. J. J. Bussgang. Crosscorrelation functions of amplitude-distorted Gaussian signals. Technical Report 216, MIT Research Laboratory of Electronics, Cambridge, Massachusetts, 1952.
6. R. D. Cook and S. Weisberg. Comments on "Sliced inverse regression for dimension reduction". Journal of the American Statistical Association, 86(414):328-332, 1991.
7. R. D. Cook, L. M. Forzani, and D. R. Tomassi. LDR: A package for likelihood-based sufficient dimension reduction. Journal of Statistical Software, 39(3), 2011.
8. M. L. Eaton. A characterization of spherical distributions. Journal of Multivariate Analysis, 20(2):272-276, 1986.
9. J. Fan and I. Gijbels. Local Polynomial Modelling and Its Applications. Chapman & Hall, 1996.
10. J. H. Friedman and W. Stuetzle. Projection pursuit regression. Journal of the American Statistical Association, 76 (376):817-823, 1981.
11. F. Giri and E. Bai, editors. Block-Oriented Nonlinear System Identification. Lecture Notes in Control and Information Sciences. Springer Verlag, 2010.
12. M. Kim and V. Pavlovic. Central subspace dimensionality reduction using covariance operators. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33 (4):657-670, 2011.
13. B. Li and S. Wang. On directional regression for dimension reduction. Journal of the American Statistical Association, 102(479):997-1008, 2007.
14. B. Li, H. Zha, and F. Chiaromonte. Contour regression: a general approach to dimension reduction. The Annals of Statistics, 33(4):1580-1616, 2005.
15. K. C. Li. Sliced inverse regression for dimension reduction. Journal of the American Statistical Association, 86(414):316-327, 1991.
16. K. C. Li. On principal Hessian directions for data visualization and dimension reduction: Another application of Stein's lemma. Journal of the American Statistical Association, 87(420): 1025-1029, 1992.
17. L. Ljung. System Identification: Theory for the User. Prentice Hall, second edition, 1999.
18. C. Lyzell and M. Enqvist. Sliced inverse regression for the identification of dynamical systems. In Proceedings of the 16th IF AC Symposium on System Identification, Brussels, Belgium, July 2012.
19. A. H. Nuttall. Theory and application of the separable class of random processes. Technical Report 343, MIT Research Laboratory of Electronics, Cambridge, Massachusetts, 1958.
20. R. K. Pearson. Discrete-Time Dynamical Models. Oxford University Press, 1999.
21. M. Schetzen. The Volterra and Wiener Theories of Nonlinear Systems. Wiley-Interscience, 1980.
22. M. Schetzen. Nonlinear system modelling and analysis from the Volterra and Wiener perspective. In F. Giri and E. Bai, editors, Block-Oriented Nonlinear System Identification, Lecture Notes in Control and Information Sciences. Springer Verlag, 2010.
23. M. Schoukens and Y. Rolain. Parametric MIMO parallel Wiener identification. In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, December 2011.
24. H. M. Wu. Kernel sliced inverse regression with applications on classification. Journal of Computational and Graphical Statistics, 17(3):590-610, 2008.
25. Y. Xia, H. Tong, W. K. Li, and L. X. Zhu. An adaptive estimation of dimension reduction subspace. Journal of the Royal Statistical Society: Series B, 64:363-410, 2002.