Non-parametric Estimation of Tsallis Entropy and Residual Tsallis Entropy Under \(\rho \) -Mixing Dependent Data

In 1988, Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, and it is non-extensive. In the present work, we propose non-parametric kernel type estimators for the Tsallis entropy and the residual Tsallis entropy, where the observations under consideration exhibit a \(\rho \) -mixing dependence condition. Asymptotic properties of the estimators are proved under suitable regularity conditions. A numerical computation of the proposed estimator is given. In addition, the asymptotic normality of the estimator is established through a broad Monte Carlo simulation study.