Part of monograph

Vajda I., Liese F.

Barnett N. ,Dragomir S. ,

Advances in Inequalities from Probability Theory and Statist

Nova Publishers

Toronto

2009

1-60021-943-8

Ing. Igor Vajda, DrSc. (ÚTIA - Oddělení stochastické informatiky)

divergence, sufficiency, testing errors, information gain,

f-divergences are studied for general probability measures and general convex functions f. Their representation by means of information gains is established and used to derive some new properties, and also to derive in a new manner some known properties. Statistical sufficiency and deficiency in the problem of testing hypotheses is characterized by means of f-divergences and the rate of convergence of the testing errors for increasing sigma-algebras is evaluated in some important cases.