Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
Probability
2020-12-22 v1
Abstract
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence on the parameters of the sum and differ only in absolute constants. The estimates obtained will be useful, in particular, when comparing two Gaussian random elements in a Hilbert space and in multidimensional central limit theorems, including the infinite-dimensional case.
Keywords
Cite
@article{arxiv.2012.10747,
title = {Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables},
author = {Sergey G. Bobkov and Alexey A. Naumov and Vladimir V. Ulyanov},
journal= {arXiv preprint arXiv:2012.10747},
year = {2020}
}
Comments
12 pages