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

09/19/2009
by   Ikhlef Bechar, et al.
Inria
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/22/2018

Two theorems on distribution of Gaussian quadratic forms

New results on comparison of distributions of Gaussian quadratic forms a...
11/01/2018

Hanson-Wright inequality in Banach spaces

We discuss two-sided bounds for moments and tails of quadratic forms in ...
09/13/2022

Sparse Hanson-Wright Inequality for a Bilinear Form of Sub-Gaussian Variables

In this paper, we derive a new version of Hanson-Wright inequality for a...
01/02/2019

An Introductory Guide to Fano's Inequality with Applications in Statistical Estimation

Information theory plays an indispensable role in the development of alg...
11/13/2019

Improved Concentration Bounds for Gaussian Quadratic Forms

For a wide class of monotonic functions f, we develop a Chernoff-style c...
05/19/2016

Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems

Bézout 's theorem states that dense generic systems of n multivariate qu...
02/17/2020

Integrating products of quadratic forms

We prove that if q_1, ..., q_m: R^n ⟶ R are quadratic forms in variable...

Please sign up or login with your details

Forgot password? Click here to reset