Abstract
Let FN and F be the empirical and limiting spectral distributions of an N × N Wigner matrix. The Cramér-von Mises (CvM) statistic is a classical goodness-of-fit statistic that characterizes the distance between FN and F in L2-norm. In this paper, we consider a mesoscopic approximation of the CvM statistic for Wigner matrices, and derive its limiting distribution. In the Appendix, we also give the limiting distribution of the CvM statistic (without approximation) for the toy model CUE. © Institute of Mathematical Statistics, 2022.
| Original language | English |
|---|---|
| Pages (from-to) | 4315-4355 |
| Journal | Annals of Applied Probability |
| Volume | 32 |
| Issue number | 6 |
| Online published | 6 Dec 2022 |
| DOIs | |
| Publication status | Published - Dec 2022 |
Funding
Z. G. Bao was partially supported by Hong Kong RGC Grant GRF 16300618, GRF 16301520 and GRF 16305421. Y. K. He was partially supported by NCCR Swissmap, SNF Grant No. 20020_1726, and CityU Start-up Grant No. 7200727.
Research Keywords
- Cramér-von Mises statistic
- empirical spectral distribution
- goodness-of-fit statistic
- Random matrices
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2022 Institute of Mathematical Statistics. Zhigang Bao. Yukun He. "On Cramér–von Mises statistic for the spectral distribution of random matrices." Ann. Appl. Probab. 32 (6) 4315 - 4355, December 2022. https://doi.org/10.1214/22-AAP1788.