Limiting spectral distribution of large dimensional Spearman's rank correlation matrices
Statistics Theory
2022-05-31 v2 Statistics Theory
Abstract
In this paper, we study the empirical spectral distribution of Spearman's rank correlation matrices, under the assumption that the observations are independent and identically distributed random vectors and the features are correlated. We show that the limiting spectral distribution is the generalized Mar\u{c}enko-Pastur law with the covariance matrix of the observation after standardized transformation. With these results, we compare several classical covariance/correlation matrices including the sample covariance matrix, Pearson's correlation matrix, Kendall's correlation matrix and Spearman's correlation matrix.
Keywords
Cite
@article{arxiv.2112.12347,
title = {Limiting spectral distribution of large dimensional Spearman's rank correlation matrices},
author = {Zeyu Wu and Cheng Wang},
journal= {arXiv preprint arXiv:2112.12347},
year = {2022}
}