Non-parametric Estimation of Tsallis Entropy and Residual Tsallis Entropy Under ρ $$\rho $$ -Mixing Dependent Data

R. Maya, M. R. Irshad (), Christophe Chesneau (), Francesco Buono () and Maria Longobardi ()
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R. Maya: Cochin University of Science and Technology, Department of Statistics
M. R. Irshad: Cochin University of Science and Technology, Department of Statistics
Christophe Chesneau: LMNO, UFR de Sciences, Université de Caen Basse-Normandie
Francesco Buono: RWTH Aachen University, Institute of Statistics
Maria Longobardi: Università degli Studi di Napoli Federico II, Dipartimento di Biologia

A chapter in Flexible Nonparametric Curve Estimation, 2024, pp 95-112 from Springer

Abstract: Abstract 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 ρ $$\rho $$ -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.

Keywords: Tsallis entropy; Residual life; ρ $$\rho $$ -mixing dependence; Kernel estimation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-66501-1_5

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DOI: 10.1007/978-3-031-66501-1_5

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