The Annals of Statistics

Comparison of Some Bounds in Estimation Theory

P. K. Sen and B. K. Ghosh

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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.

Article information

Source
Ann. Statist., Volume 4, Number 4 (1976), 755-765.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343547

Digital Object Identifier
doi:10.1214/aos/1176343547

Mathematical Reviews number (MathSciNet)
MR415858

Zentralblatt MATH identifier
0341.62025

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation

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

Citation

Sen, P. K.; Ghosh, B. K. Comparison of Some Bounds in Estimation Theory. Ann. Statist. 4 (1976), no. 4, 755--765. doi:10.1214/aos/1176343547. https://projecteuclid.org/euclid.aos/1176343547


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Corrections

  • See Correction: P. K. Sen, B. K. Ghosh. Note: Correction to "Comparison of Some Bounds in Estimation Theory". Ann. Statist., vol. 5, no. 3 (1977), 593.