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arXiv · 1911.05720

Improved Concentration Bounds for Gaussian Quadratic Forms

Robert E. Gallagher·Louis J. M. Aslett·David Steinsaltz·Ryan R. Christ
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Abstract

For a wide class of monotonic functions $f$, we develop a Chernoff-style concentration inequality for quadratic forms $Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2$, where $Z_i \sim N(0,1)$. 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.

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Robert E. Gallagher, Louis J. M. Aslett, David Steinsaltz, Ryan R. Christ. 2019-11-13. Improved Concentration Bounds for Gaussian Quadratic Forms. https://arxiv.org/abs/1911.05720

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