Maximin criterion
maximin test
A statistical test for testing a compound hypothesis :
against the compound alternative
:
, whose minimal power (cf. Power of a statistical test) is maximal in the class of all statistical tests intended for testing
against
and having the same size
,
. In statistically testing
against
a maximin invariant test exists if the problem itself is invariant relative to some group of transformations
, and there is a uniformly most-powerful test in the class of corresponding invariant tests (cf. Hunt–Stein theorem). A maximin test exists, in general, if the family of probability distributions determined by the null and competing hypotheses
and
is absolutely continuous relative to some
-finite measure.
References
[1] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1959) |
[2] | J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967) |
Maximin criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximin_criterion&oldid=32925