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).
|||E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986)|
|||S. Zacks, "The theory of statistical inference" , Wiley (1971)|
|||G.P. Klimov, "Invariant inferences in statistics" , Moscow (1973) (In Russian)|
Invariant statistic. M.S. Nikulin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Invariant_statistic&oldid=11547