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Entropy 2011, 13(4), 805-819; doi:10.3390/e13040805
Article

Large-Sample Asymptotic Approximations for the Sampling and Posterior Distributions of Differential Entropy for Multivariate Normal Distributions

1,2,3,*  and 1,2,3
1 Inserm, U678, Paris, F-75013, France 2 UPMC Univ Paris 06, UMR_S U678, Paris, F-75013, France 3 Inserm, Université de Montréal, and UPMC Univ Paris 06, LINeM, Montréal, QC, H3W 1W5, Canada
* Author to whom correspondence should be addressed.
Received: 15 February 2011 / Revised: 29 March 2011 / Accepted: 31 March 2011 / Published: 6 April 2011
Download PDF [185 KB, 24 February 2015; original version 24 February 2015]

Abstract

In the present paper, we propose a large sample asymptotic approximation for the sampling and posterior distributions of differential entropy when the sample is composed of independent and identically distributed realization of a multivariate normal distribution.
Keywords: differential entropy; large sample; asymptotic approximation; multivariate normal distribution; sampling distribution; posterior distribution; mutual information; multiinformation; total correlation; multivariate constraint
differential entropy; large sample; asymptotic approximation; multivariate normal distribution; sampling distribution; posterior distribution; mutual information; multiinformation; total correlation; multivariate constraint
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

Marrelec, G.; Benali, H. Large-Sample Asymptotic Approximations for the Sampling and Posterior Distributions of Differential Entropy for Multivariate Normal Distributions. Entropy 2011, 13, 805-819.

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