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Entropy 2010, 12(3), 338-374; doi:10.3390/e12030338

Estimation of an Entropy-based Functional

7576 Dale Ave., Saint Louis, Missouri 63117, USA
Received: 30 December 2009 / Revised: 8 February 2010 / Accepted: 24 February 2010 / Published: 3 March 2010
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Abstract

Given a function f from [0, 1] to the real line, we consider the (nonlinear) functional h obtained by evaluating the continuous entropy of the “density function” of f. Motivated by an application in signal processing, we wish to estimate h(f). Our main tool is a decomposition of h into two terms, which each have favorable scaling properties. We show that, if functions f and g satisfy a regularity condition, then the smallness of ∥fg and ∥f′g′, along with some basic control on derivatives of f and g, is sufficient to imply that h(f) and h(g) are close.
Keywords: entropy; differential entropy; Shannon entropy; entropy estimation; nonlinear functional; signal processing entropy; differential entropy; Shannon entropy; entropy estimation; nonlinear functional; signal processing
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Maurizi, B.N. Estimation of an Entropy-based Functional. Entropy 2010, 12, 338-374.

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