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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 (CC BY 3.0).

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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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