TY - GEN

T1 - Improvements on the Cramer-Rao bound

AU - Pillai, S. Unnikrishna

AU - Sinha, Nikhileshwar D.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:0026376920

SN - 078030033

T3 - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

SP - 3565

EP - 3568

BT - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

PB - Publ by IEEE

T2 - Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91

Y2 - 14 May 1991 through 17 May 1991

ER -