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Entropy 2010, 12(2), 262-274; doi:10.3390/e12020262

Entropy and Divergence Associated with Power Function and the Statistical Application

The Institute of Statistical Mathematics, Tachikawa, Tokyo 190-8562, Japan
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Received: 29 December 2009 / Revised: 20 February 2010 / Accepted: 23 February 2010 / Published: 25 February 2010
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
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Abstract

In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performance, which is known to be easily broken down in the presence of a small degree of model uncertainty. To deal with this problem, a new statistical method, closely related to Tsallis entropy, is proposed and shown to be robust for outliers, and we discuss a local learning property associated with the method.
Keywords: Tsallis entropy; projective power divergence; robustness Tsallis entropy; projective power divergence; robustness
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Eguchi, S.; Kato, S. Entropy and Divergence Associated with Power Function and the Statistical Application. Entropy 2010, 12, 262-274.

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