Decoupling and randomization for double-indexed permutation statistics
Mingxuan Zou, Jingfan Xu, Peng Ding, and Fang Han
TL;DR
This paper develops decoupling and randomization techniques to derive concentration inequalities for double-indexed permutation statistics, with applications to combinatorial inequalities and various statistical methods.
Contribution
It introduces novel decoupling and randomization methods specifically for double-indexed permutation statistics, leading to new combinatorial concentration inequalities.
Findings
New combinatorial Hanson-Wright inequality
New combinatorial Bennett inequality
Applications to rank-based, graph-based, and causal inference statistics
Abstract
This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and a new combinatorial Bennett inequality. Several illustrative examples from rank-based statistics, graph-based statistics, and causal inference are also provided.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Random Matrices and Applications · Statistical Methods and Bayesian Inference