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In this paper, we improve known results on the convergence rates of spectral distributions of large dimensional sample covariance matrices of size p n. Depending on the limiting value y of the ratio p=n and by using the tool of Stieltjes transforms, we first prove that the expected spectral distribution converges to the limiting Marčenko-Pastur distribution… (More)

In this paper, assuming p/n → 0 as n → ∞, we will prove the weak and strong convergence to the semicircle law of the empirical spectral distribution of the Hadamard product of a normalized sample covariance matrix and a sparsing matrix, which is of the form A p = 1 √ np are independent and the entries of X m,n (m × n) are independent, the matrix D m (m × m)… (More)

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