Moment inequalities for matrix-valued U-statistics of order 2
Stanislav Minsker, Xiaohan Wei
TL;DR
This paper develops new moment and concentration inequalities for matrix-valued U-statistics of order 2, utilizing advanced non-commutative probability tools, with potential applications in matrix analysis and statistics.
Contribution
Introduces Rosenthal-type moment inequalities and matrix concentration bounds for matrix-valued U-statistics of order 2, along with a novel non-commutative Khintchine inequality for spectral norms.
Findings
Derived Rosenthal-type moment inequalities for matrix U-statistics
Established new matrix concentration inequalities for U-statistics
Developed a non-commutative Khintchine inequality for Rademacher chaos
Abstract
We present Rosenthal-type moment inequalities for matrix-valued U-statistics of order 2. As a corollary, we obtain new matrix concentration inequalities for U-statistics. One of our main technical tools, a version of the non-commutative Khintchine inequality for the spectral norm of the Rademacher chaos, could be of independent interest.
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Taxonomy
TopicsRandom Matrices and Applications · Statistical Mechanics and Entropy · Quantum Mechanics and Applications