Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables
Statistics Theory
2022-09-21 v2 Methodology
Statistics Theory
Abstract
In this paper, we derive a new version of Hanson-Wright inequality for a sparse bilinear form of sub-Gaussian variables. Our results are generalization of previous deviation inequalities that consider either sparse quadratic forms or dense bilinear forms. We apply the new concentration inequality to testing the cross-covariance matrix when data are subject to missing. Using our results, we can find a threshold value of correlations that controls the family-wise error rate. Furthermore, we discuss the multiplicative measurement error case for the bilinear form with a boundedness condition.
Cite
@article{arxiv.2209.05685,
title = {Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables},
author = {Seongoh Park and Xinlei Wang and Johan Lim},
journal= {arXiv preprint arXiv:2209.05685},
year = {2022}
}