A general partial Cram\'{e}r's condition for Edgeworth expansion of a function of sample means with applications
Abstract
A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cram\'{e}r's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion for the distribution function of these functions of sample means. Additionally, we apply the proposed theorems to several specific statistics. In particular, by verifying the GPCC, we demonstrate for the first time the validity of the formal Edgeworth expansion of Pearson's correlation coefficient between random variables with absolutely continuous and discrete components. Furthermore, we conduct a series of simulation studies that show the Edgeworth expansion has higher accuracy.
Keywords
Cite
@article{arxiv.2511.01603,
title = {A general partial Cram\'{e}r's condition for Edgeworth expansion of a function of sample means with applications},
author = {Yashi Wei and Jiang Hu and Zhidong Bai},
journal= {arXiv preprint arXiv:2511.01603},
year = {2025}
}
Comments
Accepted for publication in AAP