Hanson-Wright inequality in Banach spaces
Probability
2020-10-27 v3 Functional Analysis
Statistics Theory
Statistics Theory
Abstract
We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds up to additional logarithmic factors. Moreover in a certain class of Banach spaces (including -spaces) these logarithmic factors may be eliminated. As a corollary we derive upper bounds for tails and moments of quadratic forms in subgaussian random variables, which extend the Hanson-Wright inequality.
Cite
@article{arxiv.1811.00353,
title = {Hanson-Wright inequality in Banach spaces},
author = {Radosław Adamczak and Rafał Latała and Rafał Meller},
journal= {arXiv preprint arXiv:1811.00353},
year = {2020}
}
Comments
MSC classification and acknowledgement added, minor typo corrected, references updated