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.
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}
}