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Shannon Entropy Estimation for Linear Processes

Author

Listed:
  • Timothy Fortune

    (Department of Statistics, University of Connecticut, Storrs, CT 06269, USA)

  • Hailin Sang

    (Department of Mathematics, University of Mississippi, University, MS 38677, USA)

Abstract

In this paper, we estimate the Shannon entropy S ( f ) = − E [ log ( f ( x ) ) ] of a one-sided linear process with probability density function f ( x ) . We employ the integral estimator S n ( f ) , which utilizes the standard kernel density estimator f n ( x ) of f ( x ) . We show that S n ( f ) converges to S ( f ) almost surely and in Ł 2 under reasonable conditions.

Suggested Citation

  • Timothy Fortune & Hailin Sang, 2020. "Shannon Entropy Estimation for Linear Processes," JRFM, MDPI, vol. 13(9), pages 1-13, September.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:9:p:205-:d:410890
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    References listed on IDEAS

    as
    1. Yousri Slaoui, 2014. "Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-11, June.
    2. Tran, Lanh Tat, 1992. "Kernel density estimation for linear processes," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 281-296, June.
    3. Toshio Honda, 2000. "Nonparametric Density Estimation for a Long-Range Dependent Linear Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 599-611, December.
    4. Yousri Slaoui, 2018. "Bias reduction in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 505-522, April.
    5. Hailin Sang & Yongli Sang & Fangjun Xu, 2018. "Kernel Entropy Estimation for Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 563-591, July.
    6. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
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