Exact lower and upper bounds for Gaussian measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 607-617
Voir la notice de l'article provenant de la source Math-Net.Ru
Exact upper and lower bounds on the ratio
$\operatorname{\mathbf{E}}w(\mathbf{X}-\mathbf{v})/\operatorname{\mathbf{E}}w(\mathbf{X})$ for a centered
Gaussian random vector $\mathbf{X}$ in $\mathbf{R}^n$ are obtained, as well as bounds on
the rate of change of $\operatorname{\mathbf{E}}w(\mathbf{X}-t\mathbf{v})$ in $t$, where
$w\colon\mathbf{R}^n\to[0,\infty)$ is any even unimodal function and
$\mathbf{v}$ is any vector in $\mathbf{R}^n$. As a corollary of such results,
exact upper and lower bounds on the power function of statistical tests for
the mean of a multivariate normal distribution are given.
Keywords:
Gaussian measures, multivariate normal distribution, shifts, unimodality, logconcavity, monotonicity, exact bounds, tests for the mean.
@article{TVP_2022_67_3_a11,
author = {I. Pinelis},
title = {Exact lower and upper bounds for {Gaussian} measures},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {607--617},
publisher = {mathdoc},
volume = {67},
number = {3},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a11/}
}
I. Pinelis. Exact lower and upper bounds for Gaussian measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 607-617. http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a11/