FROM THE LIKELIHOOD MAP TO EUCLIDEAN MINIMAL
SUFFICIENCY
D. A. S. Fraser
Philip McDunnough
Amir Naderi
André Plante
Abstract: We use the minimal sufficiency of the likelihood map (Fraser et al. [9]) to show the
existence of a minimal sufficient statistic with Euclidean range under weak regularity
conditions, and to extend a well-known theorem due to Barndorff-Nielsen et al. [2]. Examples
of minimal sufficient statistics are given in problems having either a restricted parameter
space or a truncated error distribution.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -