No. 998

Title:

On the conditions for the existence of ancillary
statistics in a curved exponential family

Author(s):

Masayuki, Kumon (Risk Analysis Research Center, Institute of Statistical Mathematics)

Key words:

Affine transformation, ancillary statistics, curved exponential family, cut, homogeneous space, maximal invariant, transformation family.

Abstract:

    We present necessary and sufficient conditions for the existence of ancillary statistics in a curved exponential family under some regularity conditions. When they exist, we also provide the method of constructing the ancillary statistics. The usefulness of our results are demonstrated by a lot of examples. Through main results and subsequent examples, we clarify that the group structure generated in a differential geometrical way plays an essential role for the ancillarity in a curved exponential family.