Invariant statistic
From Encyclopedia of Mathematics
A statistic taking constant values on orbits generated by a group of one-to-one measurable transformations of the sample space. Thus, if 
is the sample space, 
is a group of one-to-one 
-measurable transformations of 
onto itself and 
is an invariant statistic, then 
for all 
and 
. Invariant statistics play an important role in the construction of invariant tests (cf. Invariant test; Invariance of a statistical procedure).
References
| [1] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986) |
| [2] | S. Zacks, "The theory of statistical inference" , Wiley (1971) |
| [3] | G.P. Klimov, "Invariant inferences in statistics" , Moscow (1973) (In Russian) |
How to Cite This Entry:
Invariant statistic. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_statistic&oldid=47418
Invariant statistic. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_statistic&oldid=47418
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article