Improved Concentration Bounds for Gaussian Quadratic Forms

11/13/2019

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by   Robert E. Gallagher, et al.

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For a wide class of monotonic functions f, we develop a Chernoff-style concentration inequality for quadratic forms Q_f ∼∑_i=1^n f(η_i) (Z_i + δ_i)^2, where Z_i ∼ N(0,1). The inequality is expressed in terms of traces that are rapid to compute, making it useful for bounding p-values in high-dimensional screening applications. The bounds we obtain are significantly tighter than those that have been previously developed, which we illustrate with numerical examples.