Information Geometry of smooth densities on the Gaussian space: Poincar\'e inequalities
Statistics Theory
2021-01-11 v2 Statistics Theory
Abstract
We derive bounds for the Orlicz norm of the deviation of a random variable defined on from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the gradient. Applications to non-parametric Information Geometry are discussed.
Cite
@article{arxiv.2002.12871,
title = {Information Geometry of smooth densities on the Gaussian space: Poincar\'e inequalities},
author = {Giovanni Pistone},
journal= {arXiv preprint arXiv:2002.12871},
year = {2021}
}
Comments
Accepted. Minor corrections