Comparison of Some Bounds in Estimation Theory

P. K. Sen; B. K. Ghosh

doi:10.1214/aos/1176343547

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Home > Journals > Ann. Statist. > Volume 4 > Issue 4 > Article

July, 1976 Comparison of Some Bounds in Estimation Theory

P. K. Sen, B. K. Ghosh

Ann. Statist. 4(4): 755-765 (July, 1976). DOI: 10.1214/aos/1176343547

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Abstract

Conditions are given for the attainment of the Hammersley-Chapman-Robbins bound for the variance of an unbiased estimator, in both regular and nonregular cases. Comparisons are made between this bound and the Bhattacharyya system of bounds for a wide class of distributions and parametric functions. Sufficient conditions are provided to determine when one bound is sharper than the other one.

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P. K. Sen. B. K. Ghosh. "Comparison of Some Bounds in Estimation Theory." Ann. Statist. 4 (4) 755 - 765, July, 1976. https://doi.org/10.1214/aos/1176343547

Information

Published: July, 1976

First available in Project Euclid: 12 April 2007

zbMATH: 0341.62025

MathSciNet: MR415858

Digital Object Identifier: 10.1214/aos/1176343547

Subjects:

Primary: 62F10

Keywords: Bhattacharyya bounds , Cramer-Rao bound , exponential families , Hammersley-Chapman-Robbins bound , nonregular families , UMVU estimators , unbiased estima