# 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. M.S. Nikulin (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Invariant_statistic&oldid=11547

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098