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Biometrika 1974 61(1):137-142; doi:10.1093/biomet/61.1.137
© 1974 by Biometrika Trust
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The convergence of Bhattacharyya bounds

B. J. N. BLIGHT1 and P. V. RAO2

1Department of Statistics Birkbeck College, London
2Department of Statistics, University of Florida Gainesville

Bhattacharyya bounds are considered for the unbiased estimation of a parametric function when the sampling distribution is a member of an exponential family of distributions. It is shown that the Bhattacharyya bounds converge to the variance of the best unbiased estimator. The application of this result to variance determination in demonstrated with examples from the negative binomial distribution and from the exponential distribution in a reliability theory context.

Key Words: Bhattacharyya bounds • Bhattacharyya function • Bhattacharyya matrix • Expomential family • Negative binomial • Reliability function • Unbiased estimation


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