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November, 1975 Estimating Generating Functions
M. H. Hoyle
Ann. Statist. 3(6): 1361-1363 (November, 1975). DOI: 10.1214/aos/1176343291


This note shows that, under appropriate conditions, if a function $A(\theta; t)$ of an unknown parameter $\theta$ and a real variable $t$ has an infinite series expansion and if there is a function $B(S; t)$ of the sufficient statistic $S$ which is an unbiased estimator of $A$ for every $t$ and which also has an infinite series expansion, then the coefficients of the power of $t$ in the expansion of $B$ are the proper estimators for the coefficients of the corresponding powers in the expansion of $A$. This result is applied to estimate two functions of the normal parameters, $\mu$ and $\sigma^2$, which arise in the derivation of expressions for the removal of transformation bias.


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M. H. Hoyle. "Estimating Generating Functions." Ann. Statist. 3 (6) 1361 - 1363, November, 1975.


Published: November, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0329.62026
MathSciNet: MR386120
Digital Object Identifier: 10.1214/aos/1176343291

Primary: 62F10
Secondary: 60E05

Keywords: generating functions , infinite series expansion , sufficient statistics , Transformation bias , unbiased estimation

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 6 • November, 1975
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