### 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 language | English (US) |
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Title of host publication | Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing |

Publisher | Publ by IEEE |

Pages | 3565-3568 |

Number of pages | 4 |

Volume | 5 |

ISBN (Print) | 078030033 |

State | Published - 1991 |

Event | Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91 - Toronto, Ont, Can Duration: May 14 1991 → May 17 1991 |

### Other

Other | Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91 |
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City | Toronto, Ont, Can |

Period | 5/14/91 → 5/17/91 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Improvements on the Cramer-Rao bound

AU - Pillai, 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.

UR - http://www.scopus.com/inward/record.url?scp=0026376920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026376920&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026376920

SN - 078030033

VL - 5

SP - 3565

EP - 3568

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

PB - Publ by IEEE

ER -