Estimation of Rényi entropy of order α based on the nearest neighbor distance

In this paper, we propose a novel estimation method of the Rényi entropy of order α(≥ 2) with the minimum implementation cost. Especially, for the case of α = 2, it turns out that Rényi entropy can be simply estimated by checking the number of reoccurring the same symbol subsequently (the collision event). This makes the implementation of estimation method very simple and thus it is suitable for the applications with stringent resource restrictions.