Higher order Cramer-Rao bounds and UMVUEs

Unnikrishna Pillai, Nikhileshwar D. Sinha

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

Abstract

This work addresses the situation associated with weak Cramer-Rao (C-R) bounds and shows that it is possible to improve the C-R bound by incorporating higher order derivatives of the joint pdf such that the sequence (of bounds) so generated converges to a definite limit. Further, the limit so obtained is shown to coincide with the variance of the actual uniformly minimum variance unbiased estimator (UMVUE) for that parameter, provided the underlying pdf is of the Korpman-Darmois exponential family. Interestingly, under these conditions, 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 extremely useful, since this procedure only involves first and higher order derivatives of the joint pdf and their cross covariances.

Original languageEnglish (US)
Title of host publicationConference Record - Asilomar Conference on Circuits, Systems & Computers
PublisherPubl by Maple Press, Inc
Pages769-773
Number of pages5
Volume2
StatePublished - 1991
Event24th Asilomar Conference on Signals, Systems and Computers Part 2 (of 2) - Pacific Grove, CA, USA
Duration: Nov 5 1990Nov 7 1990

Other

Other24th Asilomar Conference on Signals, Systems and Computers Part 2 (of 2)
CityPacific Grove, CA, USA
Period11/5/9011/7/90

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Cramer-Rao bounds
Derivatives

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Pillai, U., & Sinha, N. D. (1991). Higher order Cramer-Rao bounds and UMVUEs. In Conference Record - Asilomar Conference on Circuits, Systems & Computers (Vol. 2, pp. 769-773). Publ by Maple Press, Inc.

Higher order Cramer-Rao bounds and UMVUEs. / Pillai, Unnikrishna; Sinha, Nikhileshwar D.

Conference Record - Asilomar Conference on Circuits, Systems & Computers. Vol. 2 Publ by Maple Press, Inc, 1991. p. 769-773.

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

Pillai, U & Sinha, ND 1991, Higher order Cramer-Rao bounds and UMVUEs. in Conference Record - Asilomar Conference on Circuits, Systems & Computers. vol. 2, Publ by Maple Press, Inc, pp. 769-773, 24th Asilomar Conference on Signals, Systems and Computers Part 2 (of 2), Pacific Grove, CA, USA, 11/5/90.
Pillai U, Sinha ND. Higher order Cramer-Rao bounds and UMVUEs. In Conference Record - Asilomar Conference on Circuits, Systems & Computers. Vol. 2. Publ by Maple Press, Inc. 1991. p. 769-773
Pillai, Unnikrishna ; Sinha, Nikhileshwar D. / Higher order Cramer-Rao bounds and UMVUEs. Conference Record - Asilomar Conference on Circuits, Systems & Computers. Vol. 2 Publ by Maple Press, Inc, 1991. pp. 769-773
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