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

2022/09/13 by Park, Seongoh, Wang, Xinlei, Lim, Johan · 1 citation
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2209.05685

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.

Cited by

• A note on the improved sparse Hanson-Wright inequalities

Related

• Sparse Hanson-Wright inequalities for subgaussian quadratic forms
• Hanson-Wright inequality and sub-gaussian concentration
• A note on the improved sparse Hanson-Wright inequalities
• A note on the Hanson-Wright inequality for random vectors with\n dependencies
• Sparse Hanson-Wright Inequalities with Applications