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Empirical limit theorems for Wiener chaos

Probability 2024-08-05 v4 Statistics Theory Statistics Theory

Abstract

We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener-It\^o integrals are established.

Keywords

Cite

@article{arxiv.2310.15462,
  title  = {Empirical limit theorems for Wiener chaos},
  author = {Shuyang Bai and Jiemiao Chen},
  journal= {arXiv preprint arXiv:2310.15462},
  year   = {2024}
}
R2 v1 2026-06-28T12:59:43.859Z