Mutual asymptotic equivalence is established within three classes of information-theoretic divergences of discrete probability distributions, namely, f-divergences of Csiszar, f-divergences of Bregman, and f-divergences of Burbea-Rao. These equivalences are used to find asymptotic distributions of the corresponding divergence statistics for testing the goodness of fit when the hypothetic distribution is uniform. All results are based on standard expansion techniques and on a new relation between the Bregman and Burbea-Rao divergences formulated in Lemma 2 of the paper.
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Pardo et al. (2003) studied this question.
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