## 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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## Citation Information

Please cite this preprint as:

Gallagher, R. E., Aslett, L. J. M., Steinsaltz, D. and Christ, R. R. (2019), Improved Concentration Bounds for Gaussian Quadratic Forms. `arXiv:1911.05720 [math.ST]`

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BibTeX:

```
@misc{Aslett2015b,
author={Gallagher, R. E. and Aslett, L. J. M. and Steinsaltz, D. and Christ, R. R.},
year={2019},
title={Improved Concentration Bounds for Gaussian Quadratic Forms},
note={\href{http://arxiv.org/abs/1911.05720}{\tt arXiv:1911.05720 [math.ST]}}
}
```

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