On the Estimation of Tsallis Entropy and a Novel Information Measure Based on Its Properties

This letter explores a plug-in estimator of second-order Tsallis entropy based on Kernel Density Estimation (KDE) and its implicit regularization process. First, it is shown that the expected value of the estimator corresponds to the entropy of an Additive White Gaussian Noise (AWGN) model. Then, we prove various relevant properties of the Tsallis entropy: It is monotonically non-decreasing under random variables addition, its derivative with respect to the Gaussian noise power is monotonically non-increasing, and it is concave in the additive noise power. From these, we derive an information metric that provides an alternative to the strategy of regularization.