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December, 1959 Some Remarks on Herbach's Paper, "Optimum Nature of the F-Test for Model II in the Balanced Case"
Werner Gautschi
Ann. Math. Statist. 30(4): 960-963 (December, 1959). DOI: 10.1214/aoms/1177706078


The purpose of this note is to present a lemma which will settle a question of completeness left open in Section 6 of the above mentioned paper [5]. We give two applications of the lemma, (i) by proving that, in addition to Herbach's results, also the standard $F$-test for $\sigma^2_{ab} = 0$ is a uniformly most powerful similar test, (ii) by pointing out that the standard form introduced in [5] together with our lemma provide convenient tools to prove that in a balanced model II design (with the usual normality assumptions) the standard estimates of variance components are minimum variance unbiased. This result is well known ([2], [3]) and it has in fact been pointed out by Graybill and Wortham [3] that a completeness argument may be used to demonstrate the minimum variance property of the usual estimators for the variance components. The present lemma shows that the estimators do indeed have the necessary completeness property. We will follow Herbach's notation throughout.


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Werner Gautschi. "Some Remarks on Herbach's Paper, "Optimum Nature of the F-Test for Model II in the Balanced Case"." Ann. Math. Statist. 30 (4) 960 - 963, December, 1959.


Published: December, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0122.36901
MathSciNet: MR110159
Digital Object Identifier: 10.1214/aoms/1177706078

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 4 • December, 1959
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