Limiting spectral distribution of large dimensional Spearman's rank correlation matrices

12/23/2021

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by   Zeyu Wu, et al.

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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 Marc̆enko-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, the Pearson's correlation matrix, the Kendall's correlation matrix and the Spearman's correlation matrix.