Weak Convergence of Random Functions Defined by The Eigenvectors of Sample Covariance Matrices

Abstract

Let {vij}, i, j= 1, 2,..., be iid symmetric random variables with, and for each n let Mn=(1/s) Vn VT n, where Vn=(vij), i= 1, 2,..., n, j= 1, 2,..., s= s (n) and as n→∞. Denote by On Λn OT n the spectral decomposition of Mn. Define X∈ D [0, 1] by where. It is shown that Xn→ D W0 as ...