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Entropy 2012, 14(5), 892-923; doi:10.3390/e14050892
Article

An Entropic Estimator for Linear Inverse Problems

1
 and 2,*
Received: 29 February 2012; in revised form: 2 April 2012 / Accepted: 17 April 2012 / Published: 10 May 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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Abstract: In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists), and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.
Keywords: maximun entropy method; generalized entropy estimator; information-theoretic methods; parameter estimation; inverse problems maximun entropy method; generalized entropy estimator; information-theoretic methods; parameter estimation; inverse problems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Golan, A.; Gzyl, H. An Entropic Estimator for Linear Inverse Problems. Entropy 2012, 14, 892-923.

AMA Style

Golan A, Gzyl H. An Entropic Estimator for Linear Inverse Problems. Entropy. 2012; 14(5):892-923.

Chicago/Turabian Style

Golan, Amos; Gzyl, Henryk. 2012. "An Entropic Estimator for Linear Inverse Problems." Entropy 14, no. 5: 892-923.


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