Spectra of high-dimensional Spearman correlation matrices under scale-mixture dependence
尺度混合依赖下高维 Spearman 相关矩阵的谱
We study the asymptotic spectral properties of high-dimensional Spearman correlation matrices for scale-mixture data. We consider observations of the form $x_t=σ_t ξ_t \in \mathbb{R}^N,$ where the coordinates of $ξ_t$ are i.i.d.\ and the scalar mixture variable $σ_t$ is shared by all coordinates. Under natural symmetry assumptions, the coordinates of $x_t$ are pairwise uncorrelated in both the Pearson and Spearman sense. Nevertheless, they are not independent when the…