关于具有横截面依赖性的 U-统计量的正态近似
偏微分方程分析
2025-03-26 v2
摘要
我们在横截面依赖性下，对非退化和退化的二阶 U-统计量在 Wasserstein 度量中的正态近似进行了建立。对于非退化情况，我们的结果扩展了最近研究关于横截面相关随机变量和数之和的渐近性质的工作。对于退化情况，由于 U-统计量核的非线性导致额外的依赖关系，这一问题更为棘手。通过对 Stein 方法的特定实现，我们在混合速率、横截面依赖结构的稀疏性以及 U-统计量核的矩条件下，推导出收敛速率。最后，我们通过对具有横截面依赖性数据的非参数化规范性检验展示了理论结果的实际应用。
引用
@article{arxiv.2411.16977,
title = {Stability analysis of hyperbolic-parabolic free boundary problems modelling biofilms},
author = {Dieudonné Zirhumanana Balike and Maria Rosaria Mattei and Luigi Frunzo},
journal= {arXiv preprint arXiv:2411.16977},
year = {2025}
}
备注
We kindly request the withdrawal of our submission due to a misunderstanding among the co-authors regarding the decision to upload the work to arXiv. Not all authors had agreed to its public release, and the submission was made based on an internal miscommunication. We regret this oversight and appreciate your assistance in addressing this matter