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

TL;DR

This paper presents a Bernstein-type inequality for quadratic forms of Gaussian variables, enabling uniform control and improved model selection in linear regression and inverse problems.

Contribution

The paper introduces a new Bernstein-type inequality specifically for quadratic forms of Gaussian variables, broadening tools for statistical analysis and model selection.

Findings

Provides a sharp inequality for quadratic forms of Gaussian variables

Enables improved model selection criteria in linear regression

Potentially applicable to a wider range of statistical problems

Abstract

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.