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Some optimum properties and applications of Stein's test Knight, William Rixford

Abstract

Stein's test tests the homogeneity of means of a set of normal distributions with the homoscedasticity property by means of a sequential sampling prodecure in two stages, the results of the first sample determining the size of the second. By means of this procedure a test the power of which is independent of the variance is possible. Certain extensions of Stein's test are obtained. Some optimum properties for such two stage sequential procedures are proposed, and it is shown that the tests satisfying these optimum properties are essentially the same as Stein's test.

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