Gaussian approximation of Gaussian scale mixtures

Gérard Letac; Hélène Massam

Kybernetika (2020)

  • Volume: 56, Issue: 6, page 1063-1080
  • ISSN: 0023-5954

Abstract

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For a given positive random variable V > 0 and a given Z ∼ N ( 0 , 1 ) independent of V , we compute the scalar t 0 such that the distance in the L 2 ( ℝ ) sense between Z V 1 / 2 and Z t 0 is minimal. We also consider the same problem in several dimensions when V is a random positive definite matrix.

How to cite

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Letac, Gérard, and Massam, Hélène. "Gaussian approximation of Gaussian scale mixtures." Kybernetika 56.6 (2020): 1063-1080. <http://eudml.org/doc/297110>.

@article{Letac2020,
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.},
author = {Letac, Gérard, Massam, Hélène},
journal = {Kybernetika},
keywords = {mormal approximation; Gaussian scale mixture; Plancherel theorem},
language = {eng},
number = {6},
pages = {1063-1080},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Gaussian approximation of Gaussian scale mixtures},
url = {http://eudml.org/doc/297110},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Letac, Gérard
AU - Massam, Hélène
TI - Gaussian approximation of Gaussian scale mixtures
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 6
SP - 1063
EP - 1080
AB - 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.
LA - eng
KW - mormal approximation; Gaussian scale mixture; Plancherel theorem
UR - http://eudml.org/doc/297110
ER -

References

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  2. Gneiting, T., 10.1080/00949659708811867, J. Stat. Comput. Simul. 59 (1997), 375-384. DOI10.1080/00949659708811867
  3. Hardy, G. H., Wright, E. M., 10.1017/s0025557200007464, Oxford University Press, London 2008. MR2445243DOI10.1017/s0025557200007464
  4. Kolmogorov, A. N., Sulla determinazióne empirica di una légge di distribuzióne., G. Inst. Ital. Attuari 4 (1933), 83-91. 
  5. Letac, G., Massam, H., Mohammadi, R., The ratio of normalizing constants for Bayesian Gaussian model selection., arXiv 1706. 04416 (2017), revision Oct. 12th 2018. 
  6. Monahan, J. F., Stefanski, L. A., Normal Scale Mixture Approximations to F * ( z ) and Computation of the Logistic-Normal Integral., Handbook of the Logistic Distribution (N. Balakrishnan, ed.), Marcel Dekker, New York 1992. MR1093420
  7. Palmer, J. A., Kreutz-Delgado, K., Maleig, S., Dependency models based on generalized Gaussian scale mixtures., DRAFT UCSD-SCCN v1.0, Sept 7 (2011). 
  8. Stefanski, L. A., 10.1016/0167-7152(91)90181-p, Stat. Probab. Lett- 11 (1991), 69-70. MR1093420DOI10.1016/0167-7152(91)90181-p
  9. West, M., 10.1093/biomet/74.3.646, Biometrika 74 (1987), 646-648. MR0909372DOI10.1093/biomet/74.3.646

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