论文信息 - Weak Convergence of random functions defined by the eigenvectors of sample covariance matrices

Weak Convergence of random functions defined by the eigenvectors of sample covariance matrices

Let {v ij }, i, j = 1, 2,..., be i.i.d. symmetric random variables with E(v 4 11 ) 0 as n → ∞. Denote by O n Λ n O T n the spectral decomposition of M n . Define X ∈ D[0,1] by X n (t) = √n/2Σ [nt] i=1 (y 2 i ― 1/n), where (y 1 ,y 2 ,..., y n ) T =O T (±1/√n, ±1/√n,..., ± 1/√n) T . It is shown that X n → D W 0 as n → ∞, where W 0 is a Brownian bridge. This result sheds some light on the problem of describing the behavior of the eigenvectors of M n for n large and for general v 11

J. W. Silverstein

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