On Cramér-von Mises statistic for the spectral distribution of random matrices

2019/11/11 by Zhigang Bao, Yukun He, Bao, Zhigang +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1911.04151

openalex publication_date 2019/11/11 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

Let F_N 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 F_N 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.

Citations

• Mesoscopic linear statistics of Wigner matrices
• Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
• Limiting spectral distribution of renormalized separable sample covariance matrices whenp/n→0
• On the Distribution of the Roots of Certain Symmetric Matrices

Related

• New estimators of spectral distributions of Wigner matrices
• Mesoscopic linear statistics of Wigner matrices
• The limiting spectral distribution of the generalized Wigner matrix
• On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices
• Some estimates for generalized Wigner matrix linear spectral statistics