Group invariance and their use in statistics (Keynote Speaker)

Abstract

In this paper, group actions are reviewed and are illustrated with examples of relevance for statistical applications. Equivariant functions can be useful for constructing a maximal invariant statistic. We discuss construction of maximal invariants based on a given equivariant function under some additional conditions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup.