Edgeworth expansions of the Kullback-Leibler information, (with J.-J. Lin and R. A. Levine), UCD Technical Report, 1999.


This paper proposes an approximation for the Kullback-Leibler information based on Edgeworth expansions. In information theory, entropy is a useful criterion for identifying a multivariate normal distribution. Comon (1994) proposed an Edgeworth-based expansion of neg-entropy in the univariate case. Based on the Edgeworth expansion of neg-entropy, a diagnosis is proposed here for checking multi-normality. Moreover, a measurement for Kullback-Leibler information is also proposed. We present numerical examples to demonstrate computational complexity and applications to diagnose multivariate normality, evaluate the differential entropy and choose the least statistically dependent basis from the wavelet packet dictionaries.

Keywords: Neg-entropy, differential entropy, cumulants, multivariate normal diagnostic, least statistically dependent basis, wavelet packet dictionary

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