## The Annals of Mathematical Statistics

### On Families of Admissible Tests

E. L. Lehmann

#### 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.

#### Article information

Source
Ann. Math. Statist., Volume 18, Number 1 (1947), 97-104.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177730496

Digital Object Identifier
doi:10.1214/aoms/1177730496

Mathematical Reviews number (MathSciNet)
MR22057

Zentralblatt MATH identifier
0031.37101

JSTOR

#### Citation

Lehmann, E. L. On Families of Admissible Tests. Ann. Math. Statist. 18 (1947), no. 1, 97--104. doi:10.1214/aoms/1177730496. https://projecteuclid.org/euclid.aoms/1177730496