Kybernetika 56 no. 6, 1063-1080, 2020

Gaussian approximation of Gaussian scale mixtures

Gérard Letac and Hélène MassamDOI: 10.14736/kyb-2020-6-1063

Abstract:

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.

Keywords:

mormal approximation, Gaussian scale mixture, Plancherel theorem

Classification:

62H17, 62H10

paper.pdf

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