On generalized sub-Gaussian canonical processes and their applications

Yiming Chen, Yuxuan Wang and Kefan Zhu

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 24, 7690-7707

Abstract: We obtain the upper bound of the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d. case, and we further get a tighter bound of concentration inequality through uniformly randomized techniques. A concentration inequality is derived as an extension for general functions involving independent random variables, where all components satisfy a generalized sub-Gaussian assumption. As for applications, we derive convergence results for principal component analysis and the Rademacher complexity method.

Date: 2025
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DOI: 10.1080/03610926.2025.2481104

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