Pith. sign in

REVIEW 1 cited by

Tail Bounds for Canonical $U$-Statistics and $U$-Processes with Unbounded Kernels

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2504.01318 v2 pith:H6WQN5NE submitted 2025-04-02 math.ST math.PRstat.TH

Abhishek Chakrabortty , Arun K. Kuchibhotla This is my paper · ORCID
classification math.STmath.PRstat.TH
keywords tailkernelsstatisticsunderbehaviorboundscanonicalliterature
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

In this paper, we prove exponential tail bounds for canonical (or degenerate) $U$-statistics and $U$-processes under exponential-type tail assumptions on the kernels. Most of the existing results in the relevant literature often assume bounded kernels or obtain sub-optimal tail behavior under unbounded kernels. We obtain sharp rates and optimal tail behavior under sub-Weibull kernel functions. Some examples from nonparametric and semiparametric statistics literature are considered.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms

    math.ST 2026-07 conditional novelty 6.0 of 10

    Same-sample stabilized HOIF estimators for bilinear forms are √n-CAN for k=o(n) and more numerically stable than sample-split empirical HOIFs.

Pith tools