Efficiency of entropy testing
Peter Harremoës, Igor Vajda · 2008
Recently it was shown that Shannon entropy is more Bahadur efficient than any Rényi entropy of order α ≫ 1. In this paper we shall show that relative Bahadur efficiency between any two Rényi entropies of orders α ∈ ]0; 1] is 1 when the relative Bahadur efficiency is defined according to [1]. Despite the fact that the relative Bahadur efficiency is 1 it is shown that in a certain sense Shannon entropy is more efficient than Rényi entropy for α ∈ ]0; 1]. This indicates that the definition of relative efficiency given in [1] does not fully capture the notion of efficiency.