  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.
