The asymptotic CRLB for the spectrum of ARMA processes

IEEE Transactions on Signal Processing

Volumn 51, Issue 6, 2003, Pages 1520-1531

  Ninness, Brett ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

ARMA modeling; Cr mer Rao bound; Maximum likelihood estimation; Spectrum estimation

Indexed keywords

APPROXIMATION THEORY; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; SPECTRUM ANALYSIS;

SPECTRUM ESTIMATION;

SIGNAL PROCESSING;

EID: 0037983630     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2003.811244     Document Type: Article

References (26)

1. N. Aronszajn, "Theory of reproducing kernels," Acta Mathematics, pp. 337-404, 1950.
2. K. Berk, "Consistent autoregressive spectral estimates," Ann. Statist., vol. 2, pp. 489-502, 1974.
3. J. W. Brewer, "Kronecker products and matrix calculus in system theory," IEEE Trans. Circuits Syst., vol. 25, pp. 772-781, 1978.
4. D. R. Brillinger, Time Series: Data Analysis and Theory. San Francisco, CA: Holden-Day, 1981.
5. P. Caines, Linear Stochastic Systems. New York: Wiley, 1988.
6. P. Davis, Interpolation and Approximation. London, U.K.: Blaisdell, 1963.
7. U. Forsell and L. Ljung, "Closed-loop identification revisited," Automatica, vol. 53, pp. 1215-1241, 1999.
8. B. Friedlander and B. Porat, "On the computation of an asymptotic bound for estimating autoregressive signals in white noise," Signal Process., vol. 8, pp. 291-302, 1985.
9. E. Hannan and M. Deistler, The Statistical Theory of Linear Systems. New York: Wiley, 1988.
10. E. Hannan and B. Wahlberg, "Convergence rates for inverse Toeplitz matrix forms," J. Multivariate Anal., vol. 31, pp. 127-135, 1989.
11. K. Hoffman, Banach Spaces of Analytic Functions. Englewood Cliffs, NJ: Prentice Hall, 1962.
12. S. M. Kay, Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1987.
13. L. Ljung, System Identification: Theory for the User, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1999.
14. _, "Convergence analysis of parametric identification methods," IEEE Trans. Automal. Contr., vol. AC-23, pp. 770-783, 1978.
15. _, "Asymptotic variance expressions for identified black-box transfer function models," IEEE Trans. Automat. Contr., vol. AC-30, pp. 834-844, 1985.
16. L. Ljung and P. E. Caines, "Asymptotic normality of prediction error estimators for approximate system models," Stochastics, vol. 3. pp. 29-46, 1979.
17. B. Ninness and F. Gustafsson, "A unifying construction of orthonormal bases for system identification," IEEE Trans. Automat. Contr., vol. 42, pp. 515-521, Apr. 1997.
18. P. M. J. Van den Hof, P. S. C. Heuberger, and J. Bokor, "System identification with generalized orthonormal basis functions," Automatica, vol. 31, pp. 1821-1834, 1995.
19. M. Priestley, Spectral Analysis and Time Series. New York: Academic, 1981.
20. P. Stoica and R. Moses. Introduction to Spectral Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1997.
21. T. Söderström and P. Stoica, System Identification. Englewood Cliffs, NJ: Prentice-Hall, 1989.
22. B. Wahlberg, "System identification using Laguerre models," IEEE Trans. Automat. Contr., vol. 36, pp. 551-562, May 1991.
23. _. "System identification using Kautz models," IEEE Trans. Automat. Contr., vol. 39, pp. 1276-1282, June 1994.
24. L. L. Xie and L. Ljung, "Variance expressions for spectra estimated using auto-regression," J. Econometr., 2002, to be published.
25. Z. Yuan and L. Ljung, "Black box identification of multivariable transfer functions: Asymptotic properties and optimal input design," Int. J. Contr., vol. 40, pp. 233-256, 1984.
26. Y. Zhu, "Estimation of transfer functions: Asymptotic theory and a bound of model uncertainty," Int. J. Contr., vol. 49, pp. 2241-2258, 1989.