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- W2048794119 abstract "Let $S_n=frac{1}{n}X_nX_n^*$ where $X_n={X_{ij}}$ is a $ptimes n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(mathbf {t}_1,mathbf {t}_2,sigma)=sqrt{p}({mathbf {x}}_n(mathbf {t}_1)^*(S_n+sigma I)^{-1}{mathbf {x}}_n(mathbf {t}_2)-{mathbf {x}}_n(mathbf {t}_1)^*{mathbf {x}}_n(mathbf {t}_2)m_n(sigma))$ in which $sigma>0$ and $m_n(sigma)=intfrac{dF_{y_n}(x)}{x+sigma}$ where $F_{y_n}(x)$ is the Marv{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $ntoinfty$, and ${mathbf {x}}_n(mathbf {t}_1)$ and ${mathbf {x}}_n(mathbf {t}_2)$ are unit vectors in ${Bbb{C}}^p$, having indices $mathbf {t}_1$ and $mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(mathbf {t}_1,mathbf {t}_2,sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix." @default.
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- W2048794119 date "2011-10-01" @default.
- W2048794119 modified "2023-10-02" @default.
- W2048794119 title "Asymptotic properties of eigenmatrices of a large sample covariance matrix" @default.
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- W2048794119 doi "https://doi.org/10.1214/10-aap748" @default.
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