On the eigenvectors of large dimensional sample covariance matrices

AbstractLet {vij}, i, j = 1,2, …, be i.i.d. random variables, and for each n let Mn = (1s)VnVnT, where Vn = (vij), i = 1, 2, …, n, j = 1, 2, …, s = s(n), and ns → y > 0 as n → ∞. Necessary and sufficient conditions are given to establish the convergence in distribution of certain random variables defined by Mn. When E(v114) < ∞ these variables play an important role toward understanding the behavior of the eigenvectors of this class of sample covariance matrices for n large