Theoretical Study of Multiscale Permutation Entropy on Finite-Length Fractional Gaussian Noise

Dávalos, Antonio; Jabloun, Meryem; Ravier, Philippe; Buttelli, Olivier

doi:10.23919/eusipco.2018.8553070

Cited by 13 publications

(28 citation statements)

References 12 publications

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“…Contrary to the bias in the expected value of MPE [17], the variance is strongly dependent on the pattern probabilities present in the signal, as shown in Figure 3a. For the MPE with embedded dimension d = 2, the variance of MPE has a symmetric shape around equally probable patterns.…”

Section: Discussionmentioning

confidence: 82%

“…By following on from our previous work [17], we further explored and characterized the MPE statistic. By using a Taylor series expansion, we were able to obtain an explicit expression of the MPE variance.…”

Section: Discussionmentioning

confidence: 99%

“…The calculated MPE can be interpreted as a sample statistic that estimates the true entropy value, with an associated expected value, variance, and bias, for each time scale. We have previously developed the calculation of the expected value of the MPE in [17], where the bias has been found to be independent from the pattern probabilities. We expand on this result by first proposing an explicit equation to the MPE statistic, and then we formulate the variance of MPE, as a function of the true pattern probabilities and time scale.…”

Section: Variance Of Mpe Statisticmentioning

confidence: 99%

“…However, there is still a lack of understanding regarding the statistical properties of MPE. In our previous work [17], we already derived the expected value of the MPE measurement, taking into consideration the time scale and the finite-length constraints. We found the MPE expected value to be biased.…”

Section: Introductionmentioning

confidence: 99%

“…Nonetheless, this bias depends only on the MPE parameters, and it is constant with respect to the pattern probability distribution. In practice, the MPE bias does not depend on the signal [17], and thus, can be easily corrected.…”

Section: Introductionmentioning

confidence: 99%

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On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Dávalos

Jabloun

Ravier

et al. 2019

Entropy

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Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

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Section: Discussionmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Variance Of Mpe Statisticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Dávalos

Jabloun

Ravier

et al. 2019

Entropy

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Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index

Malyarenko

Mishura

Ralchenko

et al. 2023

Fract Calc Appl Anal

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This paper is devoted to the study of the properties of entropy as a function of the Hurst index, which corresponds to the fractional Gaussian noise. Since the entropy of the Gaussian vector depends on the determinant of the covariance matrix, and the behavior of this determinant as a function of the Hurst index is rather difficult to study analytically at high dimensions, we also consider simple alternative entropy functionals, whose behavior, on the one hand, mimics the behavior of entropy and, on the other hand, is not difficult to study. Asymptotic behavior of the normalized entropy (so called entropy rate) is also studied for the entropy and for the alternative functionals.

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Identification of Permanent Faults and Disturbance Induced by Deicing Based on Permutation Entropy for the Large-Scale Clean Energy Transmission in Winter

Wang¹,

Tang²,

Xiang³

et al. 2021

Mathematical Problems in Engineering

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Ice shedding may induce isolated ground wires’ temporary grounding, which can cause electric quantities of direct current (DC) deicing devices to fluctuate. Hence, the disturbance of ice shedding is able to trigger the protective relay frequently and unnecessarily, which adversely affects the deicing process. Due to the randomness of ice shedding, the grounding resistance varies quickly; thus, the disturbance in poles of deicing devices can be detected multiple times in a short time. Moreover, the permanent fault requires steady arc plasma because of the low output voltage and current of deicing devices, which cannot bring out multiple-time disturbances in the poles. This paper proposes the identification of permanent faults and disturbance induced by deicing based on the permutation entropy, which is verified by a large number of simulations.

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Theoretical Study of Multiscale Permutation Entropy on Finite-Length Fractional Gaussian Noise

Cited by 13 publications

References 12 publications

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index

Identification of Permanent Faults and Disturbance Induced by Deicing Based on Permutation Entropy for the Large-Scale Clean Energy Transmission in Winter

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