论文信息 - Concentration of quadratic forms under a Bernstein moment assumption

Concentration of quadratic forms under a Bernstein moment assumption

A concentration result for quadratic form of independent subgaussian random variables is derived. If the moments of the random variables satisfy a "Bernstein condition", then the variance term of the Hanson-Wright inequality can be improved. The Bernstein condition is satisfied, for instance, by all log-concave subgaussian distributions.

Pierre C Bellec | P. Bellec

[1] Gábor Lugosi,et al. Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.

[2] F. T. Wright,et al. A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables , 1971 .

[3] Holger Rauhut,et al. A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[4] F. T. Wright. A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables Whose Distributions are not Necessarily Symmetric , 1973 .

[5] Maxim Sviridenko,et al. Concentration and moment inequalities for polynomials of independent random variables , 2012, SODA.

[6] F. Barthe,et al. Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems , 2012, 1202.5318.

[7] M. Rudelson,et al. Hanson-Wright inequality and sub-gaussian concentration , 2013 .

[8] M. Bagnoli,et al. Log-concave probability and its applications , 2004 .