A Note on Moment Inequality for Quadratic Forms

2014/04/04 by Xiaohui Chen, Chen, Xiaohui
Engineering · Mathematics · #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Sparse and Compressive Sensing Techniques #math.ST #msc:60F10 #msc:60F25 #stat.TH

paper · pdf · doi:10.48550/arxiv.1404.1406

12 pages, 0 figure

arxiv created 2014/05/07 · arxiv updated 2014/05/08

Abstract

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagonal structures and detect the sparsity in the high-dimensional covariance matrix are presented.

Related

• Sharp deviation bounds for quadratic forms
• Exact Estimates for Moments of Random Bilinear Forms
• CLT for random quadratic forms based on sample means and sample covariance matrices
• A note on the Hanson-Wright inequality for random vectors with dependencies
• Sparse Hanson-Wright inequalities for subgaussian quadratic forms