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Biometrika 1984 71(1):101-113; doi:10.1093/biomet/71.1.101
© 1984 by Biometrika Trust
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Bounds and expansions for Fisher information when the moments are known

R. G. JARRETT

CSIRO Division of Mathematics and Statistics Melbourne, Australia

An expansion of the score statistic as a polynomial in the random variable can be used to provide a nondecreasing sequence of lower bounds for the Fisher information when the moments are known as functions of the parameter. If the random variable is asymptotically normal, the first three bounds provide the first three terms in the asymptotic expansion for the Fisher information. This leads to a definition of efficiency which may be used to advantage with small sample sizes, providing lower bounds for the efficiency of any statistic whose moments are known but whose exact distribution is intractable.

Key Words: Asymptotic normality • Edgeworth expansion • Efficiency • Fisher information • Likelihood • Lower bound • Moment • Score statistic


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