Fisher information with respect to cumulants

IEEE Transactions on Information Theory

Volumn 50, Issue 4, 2004, Pages 638-642

  Prasad, Sudhakar ^a   Menicucci, N C ^b  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Cram r Rao lower bounds (CRLB); Cumulants; Fisher information; K statistics; Statistical estimation theory

Indexed keywords

BOUNDARY CONDITIONS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; STATISTICAL METHODS;

CRAMER-RAO LOWER BOUNDS; CUMULANTS; FISHER INFORMAT ION; K-STATISTICS; STATISTICAL ESTIMATION THEORY;

INFORMATION THEORY;

EID: 1942454268     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.825034     Document Type: Letter

References (14)

1. H. L. Van Trees, Detection, Estimation, and Modulation Theory. New York: Wiley, 1968, pt. I.
2. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991, sec. 12.11.
3. C. J. Lloyd, "Asymptotic expansions of the Fisher information in a sample mean," Statist. Probab. Lett., vol. 11, pp. 133-137, 1991.
4. E. W. Weisstein. (1999) Cumulant. [Online]. Available: http://mathworld.wolfram.com/Cumulant.html
5. J. F. Kenney and E. S. Keeping, "Cumulants and the cumulant-generating function, additive property of cumulants, and Sheppard's correction," in Mathematics of Statistics, 2nd ed. Princeton, NJ: Van Nostrand, 1951, pt. 2, sec. 4.10-4.12, pp. 77-82.
6. E. W. Weisstein, k-Statistic. [Online]. Available: http://mathworld.worldfram.com/k-Statistic.html
7. J. F. Kenney and E. S. Keeping, "The k-statistics," in Mathematics of Statistics, 3rd ed. Princeton, NJ: Van Nostrand, 1962, pt. 1, sec. 7.9, pp. 92-100.
8. P. R. Halmos, "The theory of unbiased estimation," Ann. Math. Statist., vol. 17, pp. 34-43, 1946.
9. H. H. Barrett, J. L. Denny, R. F. Wagner, and K. J. Myers, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Amer. A, vol. 12, pp. 834-852, 1995.
10. R. Bracewell, The Fourier Transforms and Its Applications, 3rd ed. New York: McGraw-Hill, 1999, pp. 257-262.
11. J. D. Gorman and A. O. Hero III, "Lower bounds for parameter estimation with constraints," IEEE Trans. Inform. Theory, vol. IT-26, pp. 1285-1301, Nov. 1990.
12. R. Narayan and R. Nityananda, "Maximum entropy restoration in astronomy," Ann. Rev. Astron. Astrophys., vol. 24, pp. 127-170, 1986.
13. T. J. Schulz, "Multi-frame blind deconvolution of astronomical images," J. Opt. Soc. Amer. A, vol. 10, pp. 1064-1073, 1993.
14. P. McCullagh, Tensor Methods in Statistics. New York: Chapman and Hall, 1987.