Gaussian Optimality for Derivatives of Differential Entropy Using Linear Matrix Inequalities †
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DOI: 10.3390/e20030182
Abstract: Let Z be a standard Gaussian random variable, X be independent of Z, and t be a strictly positive scalar. For the derivatives in t of the differential entropy of X+tZ, McKean noticed that Gaussian… read more here.
Keywords: entropy; matrix inequalities; derivatives differential; linear matrix ... See more keywords
Lower Bounds on Multivariate Higher Order Derivatives of Differential Entropy
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DOI: 10.3390/e24081155
Abstract: This paper studies the properties of the derivatives of differential entropy H(Xt) in Costa’s entropy power inequality. For real-valued random variables, Cheng and Geng conjectured that for m≥1, (−1)m+1(dm/dtm)H(Xt)≥0, while McKean conjectured a stronger statement,… read more here.
Keywords: lower bounds; derivatives differential; dtm xgt; entropy ... See more keywords