A Note on Ancillarity and Independence via Model-Preserving Transformations.

摘要

Let G be a compact group of transformations which preserves a family rho of probability measures. Let T be a statistic such that its space Tau is a G-space. If T is equivariant and G is transitive on Tau then T is ancillary for rho and distributed independently of a maximal G-invariant statistic T* which also happens to be sufficient for rho. This result in then extended to a group G satisfying the Hunt-Stein Condition.