Non-asymptotic confidence region construction in metric spaces

Haojie Dong, Huiming Zhang and Yuanyuan Zhang ()
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Haojie Dong: Soochow University
Huiming Zhang: Beihang University
Yuanyuan Zhang: Soochow University

Statistical Papers, 2025, vol. 66, issue 6, No 16, 36 pages

Abstract: Abstract Recent advancements in non-asymptotic inference have significantly impacted modern statistics and machine learning. In this paper, we utilize sub-Gaussian and sub-exponential concentration inequalities to quantify the uncertainty of random elements within general metric spaces. Specifically, utilizing these inequalities, we construct non-asymptotic confidence regions for the unbounded, asymmetric, and independent centered random vectors in Hilbert spaces. An improved symmetrization inequality guarantees tighter upper bounds for these vectors. Moreover, we establish non-asymptotic confidence regions for the unbounded, independent centered random vectors in general metric spaces. Furthermore, we establish finite sample theory under mild and finite moment conditions and create model-free confidence regions using robust median-of-mean estimators. Both simulated and empirical studies show that the proposed confidence regions significantly outperform those based on the sample mean.

Keywords: Non-asymptotic analysis; Concentration inequalities; Median-of-mean; Metric spaces; Sub-Gaussian and sub-exponential norm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01756-0

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