Let $\mathbf{Z}$ be a normal random vector in $R^k$ and let $\mathbf{1}$ be the element of $R^k$ with equal components 1. Let $X$ be a random variable that is independent of $\mathbf{Z}$ and consider the sum $\mathbf{Z} + X\mathbf{1}$. The latter has a normal distribution in $R^k$ if and only if $X$ has a normal distribution in $R^1$. The first result of this paper is a formula for a uniform bound on the difference between the density function of $\mathbf{Z} + X\mathbf{1}$ and the density function in the case where $X$ has a suitable normal distribution. This is applied to a problem in the theory of stationary Gaussian processes which arose from the author's work on a stochastic model for the CD4 marker in the progression of HIV.
Publié le : 1994-11-14
Classification:
Gaussian process,
HIV latency time,
nonnormal translation,
normal random vector,
posterior density,
60E99,
60G15,
62E99,
92A07
@article{1177004899,
author = {Berman, Simeon M.},
title = {Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions},
journal = {Ann. Appl. Probab.},
volume = {4},
number = {4},
year = {1994},
pages = { 968-980},
language = {en},
url = {http://dml.mathdoc.fr/item/1177004899}
}
Berman, Simeon M. Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions. Ann. Appl. Probab., Tome 4 (1994) no. 4, pp. 968-980. http://gdmltest.u-ga.fr/item/1177004899/