  We propose a number of concepts and properties related to `weighted'
statistical inference where the observed data are classified in accordance with
a `value' of a sample string. The motivation comes from the concepts of
weighted information and weighted entropy that proved useful in
industrial/microeconomic and medical statistics. We focus on applications
relevant in hypothesis testing and an analysis of exponential families. Several
notions, bounds and asymptotics are established, which generalize their
counterparts well-known in standard statistical research. It includes
Stein-Sanov theorem, Pinsker's, Bretangnole-Huber and van Trees inequalities
and Kullback--Leibler, Bhattacharya, Bregman, Burbea-Rao, Chernoff, Renyi and
Tsallis divergences.
