A note on the largest eigenvalue of a large dimensional sample covariance matrix

Let {vij; i, J = 1, 2, ...} be a family of i.i.d. random variables with E(v114) = [infinity]. For positive integers p, n with p = p(n) and p/n --> y > 0 as n --> [infinity], let Mn = (1/n) Vn VnT , where Vn = (vij)1 <= i <= p, 1 <= j <= n, and let [lambda]max(n) denote the largest eigenvalue of Mn. It is shown that a.s. This result verifies the boundedness of E(v114) to be the weakest condition known to assure the almost sure convergence of [lambda]max(n) for a class of sample covariance matrices.