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March, 1947 On Families of Admissible Tests
E. L. Lehmann
Ann. Math. Statist. 18(1): 97-104 (March, 1947). DOI: 10.1214/aoms/1177730496


For each hypothesis $H$ of a certain class of simple hypotheses, a family $F$ of tests is determined such that (a) given any test $w$ of $H$ there exists a test $w'$ belonging to $F$ which has power uniformly greater than or equal to that of $w$. (b) no member of $F$ has power uniformly greater than or equal to that of any other member of $F$. The effect on $F$ of various assumptions about the set of alternatives are considered. As an application an optimum property of the known type $A_1$ tests is proved, and a result is obtained concerning the most strigent tests of the hypotheses considered.


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E. L. Lehmann. "On Families of Admissible Tests." Ann. Math. Statist. 18 (1) 97 - 104, March, 1947.


Published: March, 1947
First available in Project Euclid: 28 April 2007

zbMATH: 0031.37101
MathSciNet: MR22057
Digital Object Identifier: 10.1214/aoms/1177730496

Rights: Copyright © 1947 Institute of Mathematical Statistics


Vol.18 • No. 1 • March, 1947
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