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arXiv · 2209.05685

Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables

Seongoh Park·Xinlei Wang·Johan Lim
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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.

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Seongoh Park, Xinlei Wang, Johan Lim. 2022-09-13. Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables. https://arxiv.org/abs/2209.05685

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