A Bernstein-type inequality for stochastic processes of quadratic forms of Gaussian variables

By Ikhlef Bechar. 2009

136 citations recorded by the source corpus.

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of application can be made even broader.

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9e2dc4564b3adeb685594c15303df9627525ebf8

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In Applied Mathematics

In Finance

In Statistics and Probability

Citations in the corpus

Outage Constrained Robust Transmit Optimization for Multiuser MISO Downlinks: Tractable Approximations by Conic Optimization (2011, methodology): “[31] I. Bechar, “A Bernstein-type inequality for stochastic processes of quadratic forms of Gaussian variables,” 2009, preprint, available on http://arxiv.org/abs/0909.3595.”
A More Powerful Two-Sample Test in High Dimensions using Random Projection (2011, background): “f concentration bounds for Gaussian quadratic forms, which are stated below in Lemma 1 (see Appendix A for proof). These bounds are similar to results in the papers of Bechar, and Laurent and Massart [20, 21] (c.f. Lemma 3 in Appendix A), but have error terms involving the spectral norm as opposed t”