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Entropy 2014, 16(2), 814-824; doi:10.3390/e16020814
Article

A Note on the W-S Lower Bound of the MEE Estimation

1,* , 1
,
1
 and
2
1 Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China 2 Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA
* Author to whom correspondence should be addressed.
Received: 5 November 2013 / Revised: 7 January 2014 / Accepted: 26 January 2014 / Published: 10 February 2014
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Abstract

The minimum error entropy (MEE) estimation is concerned with the estimation of a certain random variable (unknown variable) based on another random variable (observation), so that the entropy of the estimation error is minimized. This estimation method may outperform the well-known minimum mean square error (MMSE) estimation especially for non-Gaussian situations. There is an important performance bound on the MEE estimation, namely the W-S lower bound, which is computed as the conditional entropy of the unknown variable given observation. Though it has been known in the literature for a considerable time, up to now there is little study on this performance bound. In this paper, we reexamine the W-S lower bound. Some basic properties of the W-S lower bound are presented, and the characterization of Gaussian distribution using the W-S lower bound is investigated.
Keywords: estimation; entropy; MEE estimation; W-S lower bound estimation; entropy; MEE estimation; W-S lower bound
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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Chen, B.; Wang, G.; Zheng, N.; Principe, J.C. A Note on the W-S Lower Bound of the MEE Estimation. Entropy 2014, 16, 814-824.

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