Concentration of quadratic forms under a Bernstein moment assumption

2019/01/25 by Pierre Bellec, Bellec, Pierre C · 3 citations
Economics, Econometrics and Finance · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1901.08736

openalex publication_date 2019/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A Distributionally Robust Optimization Method for Adversarial Multiple Kernel Learning
• Concentration Bounds for the Collision Estimator
• The cost-free nature of optimally tuning Tikhonov regularizers and other ordered smoothers

Related

• A note on the Hanson-Wright inequality for random vectors with\n dependencies
• Hanson-Wright inequality and sub-gaussian concentration
• An Elementary Proof of the Hanson-Wright Inequality
• On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces
• Sparse Hanson-Wright inequalities for subgaussian quadratic forms