Linear minimax regret estimation of deterministic parameters with bounded data uncertainties

IEEE Transactions on Signal Processing

Volumn 52, Issue 8, 2004, Pages 2177-2188

  Eldar, Yonina C ^a   Ben Tal, Aharon ^b   Nemirovski, Arkadi ^b  

^a IEEE   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DATA PROCESSING; DATA STRUCTURES; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; THEOREM PROVING; VECTORS;

BOUNDED DATA UNCERTAINTIES; DETERMINISTIC PARAMETER ESTIMATION; LEAST SQUARE EXTIMATOR; LINEAR ESTIMATION; LINEAR MINIMAX REGRET ESTIMATION; MEAN SQUARED ERROR; MINIMAX ESTIMATION;

SIGNAL PROCESSING;

EID: 3543077522     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2004.831144     Document Type: Article

References (30)

1. N. Wiener, The Extrapolation, Interpolation and Smoothing of Stationary Time Series. New York: Wiley, 1949.
2. A. Papoulis, Probability, Random Variables, and Stochastic Processes, Third ed. New York: McGraw-Hill, 1991.
3. K. G. Gauss, Theory of Motion of Heavenly Bodies. New York: Dover, 1963.
4. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River, NJ: Prentice-Hall, 1993.
5. A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems. Washington, DC: V.H. Winston, 1977.
6. A. E. Hoerl and R. W. Kennard, "Ridge regression: Biased estimation for nonorthogonal problems," Technometr., vol. 12, pp. 55-67, Feb. 1970.
7. L. S. Mayer and T. A. Willke, "On biased estimation in linear models," Technometr., vol. 15, pp. 497-508, Aug. 1973.
8. Y. C. Eldar and A. V. Oppenheim, "Covariance shaping least-squares estimation," IEEE Trans. Signal Processing, vol. 51, pp. 686-697, Mar. 2003.
9. P. J. Huber, "Robust estimation of a location parameter," Ann. Math. Statist., vol. 35, pp. 73-101, 1964.
10. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
11. L. Breiman, "A note on minimax filtering," Ann. Probab., vol. 1, pp. 175-179, 1973.
12. S. A. Kassam and T. L. Lim, "Robust Wiener filters," J. Franklin Inst., vol. 304, pp. 171-185, Oct./Nov. 1977.
13. H. V. Poor, "On robust Wiener filtering," IEEE Trans. Automat. Contr., vol. AC-25, pp. 521-526, June 1980.
14. K. S. Vastola and H. V. Poor, "Robust Wiener-Kolmogorov theory," IEEE Trans. Inform. Theory, vol. IT-30, pp. 316-327, Mar. 1984.
15. J. Franke, Minimax-robust prediction of discrete time series, in Z. Wahrscheinlichkeitstheorie verw. Gebiete, vol. 68, pp. 337-364, 1985.
16. G. Moustakides and S. A. Kassam, "Minimax robust equalization for random signals through uncertain channels," in Proc. 20th Annu. Allerton Conf. Commun., Contr. Comput., Oct. 1982, pp. 945-954.
17. Y. C. Eldar and N. Merhav, "A competitive minimax approach to robust estimation in linear models," IEEE Trans. Signal Processing, vol. 52, pp. 1931-1946, July 2004.
18. M. S. Pinsker, "Optimal filtering of square-integrable signals in Gaussian noise," Problems Inform. Trans., vol. 16, pp. 120-133, 1980.
19. S. A. Kassam and H. V. Poor, "Robust techniques for signal processing: a survey," Proc. IEEE, vol. 73, pp. 433-481, Mar. 1985.
20. S. Verdü and H. V. Poor, "On minimax robustness: a general approach and applications," IEEE Trans. Inform. Theory, vol. IT-30, pp. 328-340, Mar. 1984.
21. S. A. Kassam and H. V. Poor, "Robust signal processing for communication systems," IEEE Commun. Mag., vol. 21, pp. 20-28, 1983.
22. Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, ""Robust mean-squared error estimation with bounded data uncertainties," IEEE Trans. Signal Processing, to be published.
23. L. D. Davisson, "Universal noiseless coding," IEEE Trans. Inform. Theory, vol. IT-19, pp. 783-795, Nov. 1973.
24. M. Feder and N. Merhav, "Universal composite hypothesis testing: a competitive minimax approach," IEEE Trans. Inform. Theory, vol. 48, pp. 1504-1517, June 2002.
25. E. Levitan and N. Merhav, "A competitive Neyman-Pearson approach to universal hypothesis testing with applications," IEEE Trans. Inform. Theory, vol. 48, pp. 2215-2229, Aug. 2002.
26. N. Merhav and M. Feder, "Universal prediction," IEEE Trans. Inform. Theory, vol. 44, pp. 2124-2147, Oct. 1998.
27. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
28. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1968.
29. A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization, ser. MPS-SIAM Optimization, 2001.
30. D. P. Bertsekas, Nonlinear Programming, Second ed. Belmont, MA: Athena Scientific, 1999.