On a family of distributions attaining the Bhattacharyya bound |
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Authors: | Hidekazu Tanaka Masafumi Akahira |
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Institution: | (1) Institute of Mathematics, University of Tsukuba, 305-8571 Ibaraki, Japan |
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Abstract: | A family of distributions for which an unbiased estimator of a functiong(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived. Indeed, we obtain a necessary
and sufficient condition for the attainment of the second order Bhattacharyya bound for a family of mixtures of distributions
which belong to the exponential family. Furthermore, we give an example which does not satisfy this condition, but where the
Bhattacharyya bound is attainable for a non-exponential family of distributions. |
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Keywords: | Cramer-Rao bound exponential family normal mixture Bessel differential equation |
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