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 a 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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