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

In: Flexible Nonparametric Curve Estimation

Author

Listed:
  • 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)

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.

Suggested Citation

  • R. Maya & M. R. Irshad & Christophe Chesneau & Francesco Buono & Maria Longobardi, 2024. "Non-parametric Estimation of Tsallis Entropy and Residual Tsallis Entropy Under ρ $$\rho $$ -Mixing Dependent Data," Springer Books, in: Hassan Doosti (ed.), Flexible Nonparametric Curve Estimation, pages 95-112, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-66501-1_5
    DOI: 10.1007/978-3-031-66501-1_5
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