0411094 20240103182301.420060210235959.9 17 s. cav_un_epca*02567230018-9448496 (2003)1474-1490Institute of Electrical and Electronics Engineers Kullback-Leibler divergence exponential family I-projection cav_un_auth*0015571 Csiszár I. HU cav_un_auth*0101161 Matúš František UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. 12A 120 IAA1075104 GA AV ČR cav_un_auth*0001799 CEZ:AV0Z1075907 The goal of this paper is to complete results available about I-projections, reverse I-projections, and their generalized versions, with focus on linear and exponential families. Pythagorean-like identities and inequalities are revisited and generalized, and generalized maximum-likelihood estimates for exponential families are introduced. The main tool is a new concept of extension of exponential families, based on our earlier results on convex cores of measures. BD MTR http://hdl.handle.net/11104/0131181 UTIA-B 20030081 2003 cav_un_epca*0256723 IEEE Transactions on Information Theory 0018-9448 1557-9654 Roč. 49 č. 6 2003 1474 1490 Institute of Electrical and Electronics Engineers