# On Bahadur Efficiency of Power Divergence Statistics - Mathematics > Statistics Theory

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Abstract: It is proved that the information divergence statistic is infinitely moreBahadur efficient than the power divergence statistics of the orders $\alpha>1$ as long as the sequence of alternatives is contiguous with respect to thesequence of null-hypotheses and the the number of observations per binincreases to infinity is not very slow. This improves the former result inHarremo\-es and Vajda 2008 where the the sequence of null-hypotheses wasassumed to be uniform and the restrictions on on the numbers of observationsper bin were sharper. Moreover, this paper evaluates also the Bahadurefficiency of the power divergence statistics of the remaining positive orders$0< \alpha \leq 1.$ The statistics of these orders are mutuallyBahadur-comparable and all of them are more Bahadur efficient than thestatistics of the orders $\alpha > 1.$ A detailed discussion of the technicaldefinitions and conditions is given, some unclear points are resolved, and theresults are illustrated by examples.

Author: ** Peter Harremoës, Igor Vajda**

Source: https://arxiv.org/