Minimum Fisher information of moment-constrained distributions with application to robust blind identification

Signal Processing

Volumn 65, Issue 2, 1998, Pages 297-313

  Živojnović, Vojin ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; IDENTIFICATION (CONTROL SYSTEMS); INFORMATION THEORY; RANDOM PROCESSES; RICCATI EQUATIONS;

FISHER INFORMATION MEASURE MINIMIZATION;

STATISTICAL METHODS;

EID: 0032026178     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(97)00225-9     Document Type: Article

References (29)

1. D. Alspach, H. Sorenson, Nonlinear Bayesian estimation using Gaussian sum approximations, IEEE Trans. Automat. Control AC-17 (August 1972) 439-448.
2. A. Benveniste, M. Goursat, G. Ruget, Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications, IEEE Trans. Automat. Control AC-25 (June 1980) 385-399.
3. J. Borwein, A. Lewis, D. Noll, Maximum entropy reconstruction using derivative information, Part II: Computational results, J. Numer. Math. 69 (1995) 243-256.
4. J. Borwein, A. Lewis, D. Noll, Maximum entropy reconstruction using derivative information. Part I: Fisher information and convex duality, Math. Oper. Res. 21 (1996) 442-468.
5. J. Borwein, M. Limber, D. Noll, Fast heuristic methods for function reconstruction using derivative information, Applicable Anal., to appear.
6. A. Cohen, Estimation in mixtures of two normal distributions, Technometrics 9 (February 1967) 15-28.
7. H. Cramér, Mathematical Methods of Statistics, Princeton University Press, Princeton, 1951.
8. D. Donoho, On minimum entropy deconvolution, in: Applied Time Series Analysis II, Academic Press, New York, 1981.
9. D. Dowson, A. Wragg, Maximum-entropy distributions having prescribed first and second moments, IEEE Trans. Inform. Theory IT-19 (September 1973) 689-693.
10. J. Einbu, On the existence of a class of maximum-entropy probability density functions, IEEE Trans. Inform. Theory IT-23 (November 1977) 772-775.
11. R. Fisher, Theory of statistical estimation, Philosoph. Trans. Roy. Soc. London 222 (1930) 309-368.
12. P.J. Huber, Robust estimation of a location parameter, Ann. Math. Statist. 35 (1964) 73-104.
13. P.J. Huber, Robust statistics: A review, Ann. Math. Statist. 43 (1972) 1041-1067.
14. P. Huber, Robust Statistics, Wiley, New York, 1981.
15. A. Kagan, Y. Linnik, C. Rao, Characterization Problems in Mathematical Statistics, Wiley, New York, 1973.
16. E. Kamke, Differentialgleichungen I. Geest & Portig, Leipzig, 1967
17. M. Kendall, A. Stuart, The Advanced Theory of Statistics, Griffin, New York, 1952.
18. L. Ljung, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, NJ, 1987.
19. R. Martin, Robust Estimation for Time Series Autoregressions, Chapter 10., Academic Press, New York, 1979
20. R. V. Mises, Mathematical Theory of Probability and Statistics, Academic Press, New York, 1964.
21. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York, 1991.
22. T. Pham, R. deFigueiredo, Maximum likelihood estimation of a class of non-Gaussian densities with application to LP deconvolution, IEEE Trans. Acoust. Speech Signal Process. ASSP-37 (January 1989) 73-82.
23. B.T. Poljak, J.Z. Tsypkin, Robust identification, Automatica 16 (1980) 53-63.
24. H. Sorenson, D. Alspach, Recursive Bayesian estimation using Gaussian sums, Automatica 7 (1971) 465-479.
25. S.S. Stanković, B.D. Kovačević, Analysis of robust stochastic approximation algorithms for process identification, Automatica 22 (1986) 483-488.
26. H. van Trees, Detection, Estimation, and Modulation Theory, Wiley, New York, 1968.
27. A. Wragg, D. Dowson, Fitting continuous probability density functions over [0, ∞) using information theory ideas, IEEE Trans. Inform. Theory IT-16 (March 1970) 226-230.
28. V. Živojnovic, A robust accuracy improvement method for blind identification using higher order statistics, IEEE Internat. Conf. Acoust. Speech Signal Process., Minneapolis, USA, 1993, pp. 516-519.
29. V. Živojnović, Moment constrained Shannon and Fisher information: Analysis and application on blind identification, Proc. ATHOS Workshop, Edinburgh, UK, 1994.