| Title:
|
Gaussian approximation of Gaussian scale mixtures (English) |
| Author:
|
Letac, Gérard |
| Author:
|
Massam, Hélène |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
56 |
| Issue:
|
6 |
| Year:
|
2020 |
| Pages:
|
1063-1080 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
mormal approximation |
| Keyword:
|
Gaussian scale mixture |
| Keyword:
|
Plancherel theorem |
| MSC:
|
62H10 |
| MSC:
|
62H17 |
| idMR:
|
MR4199903 |
| DOI:
|
10.14736/kyb-2020-6-1063 |
| . |
| Date available:
|
2021-01-08T08:33:26Z |
| Last updated:
|
2021-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148499 |
| . |
| Reference:
|
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| Reference:
|
[2] Gneiting, T.: Normal scale mixture and probability densities..J. Stat. Comput. Simul. 59 (1997), 375-384. 10.1080/00949659708811867 |
| Reference:
|
[3] Hardy, G. H., Wright, E. M.: An Introduction to the Theory of Numbers. Sixth edition..Oxford University Press, London 2008. MR 2445243, 10.1017/s0025557200007464 |
| Reference:
|
[4] Kolmogorov, A. N.: Sulla determinazióne empirica di una légge di distribuzióne..G. Inst. Ital. Attuari 4 (1933), 83-91. |
| Reference:
|
[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. |
| Reference:
|
[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. MR 1093420 |
| Reference:
|
[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). |
| Reference:
|
[8] Stefanski, L. A.: A normal scale mixture representation of the logistic distribution..Stat. Probab. Lett- 11 (1991), 69-70. MR 1093420, 10.1016/0167-7152(91)90181-p |
| Reference:
|
[9] West, M.: On scale mixture of normal distributions..Biometrika 74 (1987), 646-648. MR 0909372, 10.1093/biomet/74.3.646 |
| . |
