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20242026
most citedFrom Sparse to Dense Functional Data: Phase Transitions from a Simultaneous Inference Perspective

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math.ST2026

Approximation Theorems for High-Dimensional Canonical U-Statistics: Gaussian Chaos and Phase Transition

Leheng Cai, Qirui Hu

We study simultaneous inference for maxima of canonical order-two -statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibratio…

math.ST2026

Asymptotic Anytime-Valid Inference for U-statistics

Leheng Cai, Qirui Hu, Weijia Li

We study asymptotic anytime-valid confidence sequences for degree-two U-statistics under continuous monitoring. In the nondegenerate case, Hoeffding's projection reduces the proble…

math.ST2026

Strong Gaussian approximation for U-statistics in high dimensions and beyond

Weijia Li, Leheng Cai, Qirui Hu

We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich…