Randomization test
permutation test
A statistical test for the hypothesis that the probability density of the random vector under observation is symmetric with respect to permutations of its arguments.
Given a realization of a random vector
, the hypothesis
to be tested is whether or not the unknown probability density of
is symmetric with respect to permutations of the arguments, that is, whether
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where is an arbitrary permutation of
. Let
and
be the vector of order statistics (cf. Order statistic) and the rank vector, respectively, constructed from
, and let a statistic
with values in
be such that for some
,
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almost-everywhere. Then the statistical test with critical function connected with
by the relation
is called a randomization test. Since
is a complete sufficient statistic, the family of similar tests (cf. Similar test) coincides with the family of permutation tests.
References
[1] | J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967) |
[2] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986) |
Randomization test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Randomization_test&oldid=15231