Datasets in a variety of disciplines require methods where both the sample size and the dataset dimensionality are allowed to be large. This framework is drastically different from the classical asymptotic framework where the number of observations is allowed to be large but the dimensionality...

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...