Geodesic
Gaussian approximation of Gaussian scale mixtures
Kybernetika, Tome 56 (2020) no. 6, pp. 1063-1080.

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For a given positive random variable $V>0$ and a given $Z\sim N(0,1)$ independent of $V$, we compute the scalar $t_0$ such that the distance in the $L^2(\mathbb{R})$ sense between $Z V^{1/2}$ and $Z\sqrt{t_0}$ is minimal. We also consider the same problem in several dimensions when $V$ is a random positive definite matrix.
DOI : 10.14736/kyb-2020-6-1063
Classification : 62H10, 62H17
Keywords: mormal approximation; Gaussian scale mixture; Plancherel theorem 
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Letac, Gérard; Massam, Hélène. Gaussian approximation of Gaussian scale mixtures. Kybernetika, Tome 56 (2020) no. 6, pp. 1063-1080. doi : 10.14736/kyb-2020-6-1063. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-6-1063/

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