ON THE DEFINITION OF PROBABILITY DENSITIES AND SUFFICIENCY
OF THE LIKELIHOOD MAP
D. A. S. Fraser
Philip McDunnough
Amir Naderi
André Plante
Abstract: The definition and sufficiency of the likelihood map are discussed in detail. It is
shown that the likelihood map is sufficient without any restriction on the family of probability
measures and that it is minimal sufficient subject to weak conditions. The paper provides a
general foundation for the use of the likelihood function and the likelihood function map in
statistical inference.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -