Wavelet Fisher’s Information Measure of 1=f α Signals

Abstract:We address the problem of non-parametric estimation of the recently proposed measures of statistical dispersion of positive continuous random variables. The measures are based on the concepts of differential entropy and Fisher information and describe the "spread" or "variability" of the random variable from a different point of view than the ubiquitously used concept of standard deviation. The maximum penalized likelihood estimation of the probability density function proposed by Good and Gaskins is applied and a complete methodology of how to estimate the dispersion measures with a single algorithm is presented. We illustrate the approach on three standard statistical models describing neuronal activity.

Section: Introductionmentioning

confidence: 99%

Nonparametric Estimation of Information-Based Measures of Statistical Dispersion

Kostal

Pokora

2012

“…Parameter q provides further analysis flexibility and allows to potentially emphasize some characteristics in the data under study. In [19], the wavelet Fisher's information was introduced and the wavelet Fisher information plane was presented. An interesting question is how the information plane is affected by the value of the parameter q.…”

Section: Wavelet Q-fisher Informationmentioning

confidence: 99%

“…Closed-form expressions are found for the wavelet q-Fisher information of scaling signals and information planes are also constructed. Wavelet q-Fisher information generalizes wavelet Fisher information [19] and provides further analysis flexibility with the parameter q. Parameter q in wavelet q-Fisher information permits to adapt the analyses to the type and characteristics of the data. Extensive experimental studies using simulated signals validate the theoretical findings.…”

Section: Introductionmentioning

confidence: 99%

Wavelet q-Fisher Information for Scaling Signal Analysis

Ramírez-Pacheco

Torres-Roman

Argaez-Xool

et al. 2012

Self Cite

This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.

“…A discrete version of Shannon wavelet entropy was proposed by [25][26][27][29][30][31][32] to characterize self-similar processes with Gaussian and stationary increments. Recently, a similar approach based on wavelet probability densities was proposed by [33] using the Fisher-Shannon method [15].…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

Nicolis

Mateu

Contreras-Reyes

2020

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.