Sufficiency and Statistical Decision Functions

Sufficiency of cut-generating functions

This note settles an open problem about cut-generating functions, a concept that has its origin in the work of Gomory and Johnson from the 1970’s and has received renewed attention in recent years.

4 Sufficiency in quantum statistical inference

This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative a...

Certain Sufficiency Conditions on Gaussian Hypergeometric Functions

The author aims at finding certain conditions on a, b and c such that the normalized Gaussian hypergeometric function zF (a, b; c; z) given by F (a, b; c; z) = ∞ ∑ n=0 (a, n)(b, n) (c, n)(1, n) z, |z| < 1, is in certain subclasses of analytic functions. A particular operator acting on F (a, b; c; z) is also discussed.

Sufficiency and Information Rate of Multi-stag^ Statistical Tests

Φ - Divergences , Sufficiency , Bayes Sufficiency , and Deficiency

The paper studies the relations between φ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of φ-divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form...