On Families of Admissible Tests

E. L. Lehmann

doi:10.1214/aoms/1177730496

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Home > Journals > Ann. Math. Statist. > Volume 18 > Issue 1 > Article

March, 1947 On Families of Admissible Tests

E. L. Lehmann

Ann. Math. Statist. 18(1): 97-104 (March, 1947). DOI: 10.1214/aoms/1177730496

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Abstract

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.