Open Access
December, 1969 Optimum Estimators for Linear Functions of Location and Scale Parameters
Nancy R. Mann
Ann. Math. Statist. 40(6): 2149-2155 (December, 1969). DOI: 10.1214/aoms/1177697292


In this paper, loss is taken to be proportional to squared error with the constant of proportionality equal to the square of the inverse of a scale parameter, and an invariant estimator is defined to be one with risk invariant under transformations of location and scale. For certain classes of estimators, best (minimum-mean-squared-error) invariant estimators are found for specified linear functions of an unknown scale parameter and one or more unknown location parameters. Even when the specified function is equal to a single location parameter, the best invariant estimator is not equal to the best unbiased estimator in the class except for complete samples from certain distributions such as the Gaussian.


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Nancy R. Mann. "Optimum Estimators for Linear Functions of Location and Scale Parameters." Ann. Math. Statist. 40 (6) 2149 - 2155, December, 1969.


Published: December, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0188.50303
MathSciNet: MR260091
Digital Object Identifier: 10.1214/aoms/1177697292

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 6 • December, 1969
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