Improvements on the Cramer-Rao bound

Unnikrishna Pillai, Nikhileshwar D. Sinha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the context of nonrandom parameter estimation from a finite set of observations, the situation associated with weak Cramer-Rao bounds is addressed. It is shown that it is possible to improve the Cramer-Rao bound by incorporating higher-order derivatives of the joint probability density function (pdf) such that the sequence (of bounds) so generated converges to a definite limit. The limit so obtained is shown to coincide with the variance of the actual uniformly minimum variance unbiased estimator (UMVUE) for this parameter, provided the underlying pdf is of the Korpman-Darmois exponential family. This technique also provides a constructive procedure to evaluate the UMVUE for any unknown parameter (or its functions) contained in the data. From a practical standpoint this is useful, since this procedure only involves the first-/and higher-order derivatives of the joint pdf and their cross covariance.

Original languageEnglish (US)
Title of host publicationProceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
PublisherPubl by IEEE
Pages3565-3568
Number of pages4
Volume5
ISBN (Print)078030033
StatePublished - 1991
EventProceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91 - Toronto, Ont, Can
Duration: May 14 1991May 17 1991

Other

OtherProceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91
CityToronto, Ont, Can
Period5/14/915/17/91

Fingerprint

Cramer-Rao bounds
probability density functions
Probability density function
estimators
Derivatives
Parameter estimation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics

Cite this

Pillai, U., & Sinha, N. D. (1991). Improvements on the Cramer-Rao bound. In Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing (Vol. 5, pp. 3565-3568). Publ by IEEE.

Improvements on the Cramer-Rao bound. / Pillai, Unnikrishna; Sinha, Nikhileshwar D.

Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. Vol. 5 Publ by IEEE, 1991. p. 3565-3568.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pillai, U & Sinha, ND 1991, Improvements on the Cramer-Rao bound. in Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. vol. 5, Publ by IEEE, pp. 3565-3568, Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91, Toronto, Ont, Can, 5/14/91.
Pillai U, Sinha ND. Improvements on the Cramer-Rao bound. In Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. Vol. 5. Publ by IEEE. 1991. p. 3565-3568
Pillai, Unnikrishna ; Sinha, Nikhileshwar D. / Improvements on the Cramer-Rao bound. Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. Vol. 5 Publ by IEEE, 1991. pp. 3565-3568
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