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On the performance of Fisher Information Measure and Shannon entropy estimators

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  • Telesca, Luciano
  • Lovallo, Michele

Abstract

The performance of two estimators of Fisher Information Measure (FIM) and Shannon entropy (SE), one based on the discretization of the FIM and SE formulae (discrete-based approach) and the other based on the kernel-based estimation of the probability density function (pdf) (kernel-based approach) is investigated. The two approaches are employed to estimate the FIM and SE of Gaussian processes (with different values of σ and size N), whose theoretic FIM and SE depend on the standard deviation σ. The FIM (SE) estimated by using the discrete-based approach is approximately constant with σ, but decreases (increases) with the bin number L; in particular, the discrete-based approach furnishes a rather correct estimation of FIM (SE) for L∝σ. Furthermore, for small values of σ, the larger the size N of the series, the smaller the mean relative error; while for large values of σ, the larger the size N of the series, the larger the mean relative error. The FIM (SE) estimated by using the kernel-based approach is very close to the theoretic value for any σ, and the mean relative error decreases with the increase of the length of the series. Comparing the results obtained using the discrete-based and kernel-based approaches, the estimates of FIM and SE by using the kernel-based approach are much closer to the theoretic values for any σ and any N and have to be preferred to the discrete-based estimates.

Suggested Citation

  • Telesca, Luciano & Lovallo, Michele, 2017. "On the performance of Fisher Information Measure and Shannon entropy estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 569-576.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:569-576
    DOI: 10.1016/j.physa.2017.04.184
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    Citations

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    Cited by:

    1. Li, Xudong & Telesca, Luciano & Lovallo, Michele & Xu, Xuan & Zhang, Jun & Song, Weiguo, 2020. "Spectral and informational analysis of pedestrian contact force in simulated overcrowding conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    2. Luciano Telesca & Michele Lovallo & Gianfranco Cardettini & Angelo Aromando & Nicodemo Abate & Monica Proto & Antonio Loperte & Nicola Masini & Rosa Lasaponara, 2023. "Urban and Peri-Urban Vegetation Monitoring Using Satellite MODIS NDVI Time Series, Singular Spectrum Analysis, and Fisher–Shannon Statistical Method," Sustainability, MDPI, vol. 15(14), pages 1-20, July.
    3. Moreno-Torres, Lucia Rebeca & Gomez-Vieyra, Armando & Lovallo, Michele & Ramírez-Rojas, Alejandro & Telesca, Luciano, 2018. "Investigating the interaction between rough surfaces by using the Fisher–Shannon method: Implications on interaction between tectonic plates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 560-565.
    4. Ba, Rui & Song, Weiguo & Lovallo, Michele & Zhang, Hui & Telesca, Luciano, 2022. "Informational analysis of MODIS NDVI and EVI time series of sites affected and unaffected by wildfires," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    5. Stosic, Tatijana & Telesca, Luciano & Stosic, Borko, 2021. "Multiparametric statistical and dynamical analysis of angular high-frequency wind speed time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    6. Guignard, Fabian & Lovallo, Michele & Laib, Mohamed & Golay, Jean & Kanevski, Mikhail & Helbig, Nora & Telesca, Luciano, 2019. "Investigating the time dynamics of wind speed in complex terrains by using the Fisher–Shannon method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 611-621.
    7. Antonio Squicciarini & Elio Valero Toranzo & Alejandro Zarzo, 2024. "A Time-Series Feature-Extraction Methodology Based on Multiscale Overlapping Windows, Adaptive KDE, and Continuous Entropic and Information Functionals," Mathematics, MDPI, vol. 12(15), pages 1-21, July.
    8. Cárdenas-Moreno, P.R. & Moreno-Torres, L.R. & Lovallo, M. & Telesca, L. & Ramírez-Rojas, A., 2021. "Spectral, multifractal and informational analysis of PM10 time series measured in Mexico City Metropolitan Area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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