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The Application of Invariance to Unbiased Estimation

Author(s): Eaton, Morris L. and Carl N. Morris
Corporate Author: Rand Coporation
Corporate Report Number: R-592-PR
Date of Publication: 1970-10
Pages: 28
Contract: F44620-67-C-0045
Project: Project Rand
AD Number: AD0714067

A relatively easy method is discussed for constructing minimum variance unbiased estimates of nonstandard parametric functions under a variety of statistical model assumptions. The most important assumption is that the family of given distributions be invariant under a group of transformations. Estimation of the reliability function of an aircraft is an important application, as is estimation of moments of transformed data. The results are applied to unbiased estimation in the multivariate normal distribution and to a problem involving U-statistics.

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