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some further results on the minimum error entropy estimation一些进一步的结果误差最小熵估计.pdf

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Entropy 2012, 14, 966-977; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Some Further Results on the Minimum Error Entropy Estimation Badong Chen 1,2,* and Jose C. Principe 2 1 Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, China 2 Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA; E-Mail: principe@ * Author to whom correspondence should be addressed; E-Mail: chenbd04@. Received: 1 April 2012; in revised form: 2 May 2012 / Accepted: 10 May 2012 / Published: 21 May 2012 Abstract: The minimum error entropy (MEE) criterion has been receiving increasing attention due to its promising perspectives for applications in signal processing and machine learning. In the context of Bayesian estimation, the MEE criterion is concerned with the estimation of a certain random variable based on another random variable, so that the error’s entropy is minimized. Several theoretical results on this topic have been reported. In this work, we present some further results on the MEE estimation. The contributions are twofold: (1) we extend a recent result on the minimum entropy of a mixture of unimodal and symmetric distributions to a more general case, and prove that if the conditional distributions are generalized uniformly dominated (GUD), the dominant alignment will be the MEE estimator; (2) we show by
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