—By extending the information-theoretic arguments of previous papers dealing with the Barron-type density estimates, and their consistency in information divergence and chi-square divergence, the problem of consistency in Csisz´ar’s -divergence is motivated for general convex functions . The problem of consistency in -divergence is solved for all with (0) < 1and
Alain Berlinet, Igor Vajda, Edward C. van der Meul